Pembrolizumab in Treating Patients With Desmoplastic Melanoma That Can or Cannot Be Removed by Surgery

Inclusion Criteria:

* COHORT A: Patients must have histologically or cytologically confirmed primary desmoplastic melanoma that is deemed resectable; the decision to perform surgery on patients must be based on good clinical judgment; eligible patients for surgical resection must have disease that, in the judgment of the surgeon, is deemed completely resectable resulting in free surgical margins; patients must have residual disease after initial biopsy which can be measurable or non-measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1; residual disease can either be confirmed with fine-needle aspiration (FNA) or if measurable disease is present, no FNA needs to be obtained OR
* COHORT B: Patients must have histologically or cytologically confirmed primary desmoplastic melanoma that is unresectable; patients in Cohort B must have measurable disease per RECIST 1.1
* Contrast-enhanced computed tomography (CT) scans of the chest, abdomen and pelvis are required; a whole body positron emission tomography (PET)/CT scan with diagnostic quality images and intravenous iodinated contrast may be used in lieu of a contrast enhanced CT of the chest, abdomen and pelvis; imaging of the head and neck is required only if the patient has a head/neck primary; contrast may be omitted if the treating investigator believes that exposure to contrast poses an excessive risk to the patient; if skin lesions are being followed as measurable disease, photograph with a ruler included and physician measurements, must be kept in the patient's chart as source documentation; all measurable lesions must be assessed within 28 days prior to registration; tests to assess non-measurable disease must be performed within 42 days prior to registration; all disease must be assessed and documented on the baseline tumor assessment form (RECIST 1.1)
* Patients must not have known brain metastases unless brain metastases have been treated and patient is asymptomatic with no residual neurological dysfunction and has not received enzyme-reducing anti-epileptic drugs or corticosteroids for at least 14 days prior to registration
* Patients must not have received prior systemic treatment for this melanoma
* Patients must not be planning to receive concomitant other biologic therapy, hormonal therapy, other chemotherapy, anti-cancer surgery or other anti-cancer therapy while on this protocol
* Patients must not have received radiation therapy, non-cytotoxic agents or investigational agents or systemic corticosteroids within 14 days prior to registration
* Patients may have received prior surgery; all adverse events associated with prior surgery must have resolved to =\< grade 1 (per Common Terminology Criteria for Adverse Events \[CTCAE\] 4.0) prior to registration
* Patients must be \>= 18 years of age
* Absolute neutrophil count (ANC) \>= 1,500/mcl (obtained within 28 days prior to registration)
* Platelets \>= 50,000/mcl (obtained within 28 days prior to registration)
* Hemoglobin \>= 8 g/dL (obtained within 28 days prior to registration)
* Total bilirubin =\< 1.5 x institutional upper limit of normal (IULN) (or =\< 3.0 x IULN with Gilbert's syndrome) (obtained within 28 days prior to registration)
* Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 x IULN (or \< 5 x IULN for patients with known liver metastases) (obtained within 28 days prior to registration)
* Patients must have lactate dehydrogenase (LDH) performed within 28 days prior to registration
* Patients must have Zubrod performance status =\< 2
* Patients must not have history of (non-infectious) pneumonitis that required steroids or current pneumonitis
* Patients must not have an active infection requiring systemic therapy
* Patients must not have active autoimmune disease that has required systemic treatment in past 2 years (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive drugs); replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment
* Patients must not have received live vaccines within 42 days prior to registration; examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, chicken pox, shingles, yellow fever, rabies, Bacillus Calmette-Guerin (BCG), and typhoid (oral) vaccine; seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (e.g., Flu-Mist) are live attenuated vaccines, and are not allowed
* Patients known to be human immunodeficiency virus (HIV) positive prior to registration are eligible if they meet the following criteria within 30 days prior to registration: stable and adequate CD4 counts (\>= 350 mm\^3), and serum HIV viral load of \< 25,000 IU/ml; patients must be on a stable anti-viral therapy
* No other prior malignancy is allowed except for the following: adequately treated basal cell or squamous cell skin cancer, adequately treated in situ cancer, adequately treated stage I or II cancer (including multiple primary melanomas) from which the patient is currently in complete remission, or any other cancer from which the patient has been disease free for three years
* Women of childbearing potential must have a negative urine or serum pregnancy test within 28 days prior to registration; women/men of reproductive potential must have agreed to use an effective contraceptive method for the course of the study through 120 days after the last dose of study medication; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately; a woman is considered to be of "reproductive potential" if she has had menses at any time in the preceding 12 consecutive months; in addition to routine contraceptive methods, "effective contraception" also includes heterosexual celibacy and surgery intended to prevent pregnancy (or with a side-effect of pregnancy prevention) defined as a hysterectomy, bilateral oophorectomy, or bilateral tubal ligation; however, if at any point a previously celibate patient chooses to become heterosexually active during the time period for use of contraceptive measures outlined in the protocol, he/she is responsible for beginning contraceptive measures; patients must not be pregnant or nursing due to unknown teratogenic side effects
* Patients must have specimens available and institutions must be planning to submit for centralized pathology review and for integrated translational medicine objectives
* Patients must be informed of the investigational nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines
* As a part of the Oncology Patient Enrollment Network (OPEN) registration process, the treating institution's identity is provided in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered in the system