Pembrolizumab in Treating Patients With Rare Tumors That Cannot Be Removed by Surgery or Are Metastatic

Inclusion Criteria:

* Be willing and able to provide written informed consent/assent for the trial
* Have measurable disease based on RECIST 1.1 or irRECIST; only cohort 9 and 10 can have evaluable disease (non-measurable lesions); tumor lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions; patients may have bone metastatic disease evaluable according to tumor evaluation criteria best suitable and accepted for the tumor type evaluated
* Have one of the following advanced (unresectable and/or metastatic) solid tumor indications that has progressed following standard therapies, where standard therapies are available:

  * Squamous cell carcinoma of the skin
  * Small cell malignancies of non-pulmonary origin
  * Adrenocortical carcinoma
  * Medullary renal cell carcinoma
  * Carcinoma of unknown primary
  * Penile carcinoma
  * Vascular sarcoma
  * Germ cell tumor
  * Paraganglioma-pheochromocytoma
  * Other rare tumors (except those tumor types listed in exclusion)
* Have failed prior treatment within 6 months of consent date
* Have biopsiable disease; subjects must have at least one lesion amenable to biopsy; tumor lesions used for biopsy should not be lesions used as target lesions; in cohort 9: paraganglioma-pheochromocytoma or cohort 10, where there is prominent bony disease, biopsies may not be possible due to the nature of the disease
* Be willing to provide archival tissue; if archival tissue is not available, or a newly obtained core or excisional biopsy of a tumor lesion will be obtained; newly-obtained is defined as a specimen obtained up to 6 weeks (42 days) prior to initiation of treatment on day 1; in cohort 9: paraganglioma-pheochromocytoma or cohort 10, where there is prominent bony disease, biopsies may not be possible due to the nature of the disease
* Have a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) performance scale
* Absolute neutrophil count (ANC) \>= 1,000/mcL (performed within 28 days of treatment initiation)
* Platelets \>= 75,000/mcL (performed within 28 days of treatment initiation)
* Hemoglobin \>= 9 g/dL or \>= 5.6 mmol/L without transfusion or erythropoietin (EPO) dependency (within 7 days of assessment) (performed within 28 days of treatment initiation)
* Serum creatinine OR measured or calculated creatinine clearance (glomerular filtration rate \[GFR\] can also be used in place of creatinine or creatinine clearance \[CrCl\]) =\< 1.5 X upper limit of normal (ULN) OR \>= 60 mL/min for subject with creatinine levels \> 1.5 X institutional ULN (performed within 28 days of treatment initiation)
* Serum total bilirubin =\< 1.5 X ULN OR direct bilirubin =\< ULN for subjects with total bilirubin levels \> 1.5 ULN (performed within 28 days of treatment initiation)
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X ULN OR =\< 5 X ULN for subjects with liver metastases (performed within 28 days of treatment initiation)
* Albumin \> 2.5 mg/dL (performed within 28 days of treatment initiation)
* International normalized ratio (INR) or prothrombin time (PT) =\< 1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or partial thromboplastin time (PTT) is within therapeutic range of intended use of anticoagulants (performed within 28 days of treatment initiation)
* Activated partial thromboplastin time (aPTT) =\< 1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants (performed within 28 days of treatment initiation)
* Female subject of childbearing potential should have a negative urine or serum pregnancy within 72 hours prior to receiving the first dose of study medication; if the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required
* Female subjects of childbearing potential should be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 120 days after the last dose of study medication; subjects of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \> 1 year
* Male subjects should agree to use an adequate method of contraception starting with the first dose of study therapy through 120 days after the last dose of study therapy
* For subjects in cohort 2 (small cell malignancies of non-pulmonary origin), confirmation of no brain metastases via imaging

Exclusion Criteria:

* Is currently participating and receiving study therapy or concurrent chemotherapy, immunotherapy, biologic, or hormonal therapy for cancer treatment at the time of administration of first dose of trial treatment; continuation of hormone replacement therapy is permitted; stable regimens of hormonal therapy i.e. for prostate cancer (e.g. leuprolide, a gonadotrophin releasing hormone \[GnRH\] agonist), ovarian, or breast cancer are not exclusionary
* Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment
* Has a known history of active TB (bacillus tuberculosis)
* Hypersensitivity to pembrolizumab or any of its excipients
* Has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to a previously administered agent; Note: subjects with =\< grade 2 neuropathy are an exception to this criterion and may qualify for the study; Note: if subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy
* Has a known additional malignancy that is progressing or requires active treatment; exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer, and diseases for which the treatment could reasonably include pembrolizumab and are not part of the excluded tumor type list or not eligible for the phase I trial
* Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis; subjects with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to trial treatment; this exception does not include carcinomatous meningitis which is excluded regardless of clinical stability
* Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs); replacement therapy (eg., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment; immunosuppressive corticosteroid doses (\> 10 mg prednisone daily or equivalent) within 4 weeks prior to the first dose of pembrolizumab; Note: corticosteroids given within 24 hours of an imaging study for purposes of pre-medication in patients with hypersensitivity to radiologic contrast agents are allowed
* Has known history of, or any evidence of active, non-infectious pneumonitis
* Has an active infection requiring systemic therapy
* Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator
* Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial
* Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment
* Has received prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent
* Has a known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies)
* Has known active hepatitis B (e.g., hepatitis B surface antigen \[HBsAg\] reactive) or hepatitis C (e.g., hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\] is detected)
* Has received a live vaccine within 30 days of planned start of study therapy; Note: seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist) are live attenuated vaccines, and are not allowed
* Is participating in cohort 10 and has melanoma; non-small cell lung cancer; hepatocellular carcinoma; Merkel cell carcinoma; colon or rectal adenocarcinoma; anal canal squamous cell carcinoma; pancreas adenocarcinoma; esophageal squamous cell carcinoma or adenocarcinoma (including gastroesophageal \[GE\] junction); biliary tract adenocarcinoma (gallbladder and biliary tree but excluding ampulla of vater cancers); carcinoid tumors; neuroendocrine carcinomas (well or moderately differentiated pancreatic neuroendocrine tumor); estrogen receptor (ER)-positive human epidermal growth factor receptor 2 (HER2)-negative breast cancer; triple negative breast cancer; ovarian epithelial, fallopian tube or primary peritoneal carcinoma; endometrial carcinoma; cervical squamous cell cancer; vulvar squamous cell carcinoma; small cell lung cancer; mesothelioma (malignant pleural mesothelioma); thyroid cancer (papillary or follicular subtype); salivary gland carcinoma; nasopharyngeal carcinoma; glioblastoma multiforme; leiomyosarcoma; prostate adenocarcinoma; gastric adenocarcinoma; or small bowel malignancy