Selinexor and Pembrolizumab for the Treatment of Cisplatin-Ineligible or Cisplatin-Refractory Locally Advanced or Metastatic Urothelial Carcinoma

Inclusion Criteria:

* Pathologically confirmed locally advanced or metastatic urothelial carcinoma by histology
* Measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) version (v)1.1
* Not eligible to receive cisplatin-based chemotherapy due to renal dysfunction (defined as creatinine clearance \[CrCl\] =\< 60 mL/min), \> grade 2 peripheral neuropathy, or ototoxicity (defined as \>= grade 2 hearing loss); OR unwillingness of patient to receive cisplatin; OR progressed on one platinum-based chemotherapy regimen for advanced disease
* May have had neoadjuvant or adjuvant platinum-based chemotherapy or intravesical therapy in the past
* \>= 18 years of age
* Eastern Cooperative Oncology Group (ECOG) performance status score of 0, 1 or 2
* Life expectancy \>= 3 months
* Absolute neutrophil count (ANC) \>= 1 × 10\^9/L
* Platelet count \>= 75 × 10\^9/L (patients for whom \<50% of bone marrow nucleated cells are plasma cells) or \>= 50,000/mm3 (patients for whom \>= 50% of bone marrow nucleated cells are plasma cells)
* Hemoglobin \>= 9 g/dL (may have been transfused)
* Total bilirubin level =\< 1.5 x the upper limit of normal (ULN) range (except patients with Gilbert's syndrome who must have a total bilirubin of \< 3 x ULN)
* Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) levels =\< 2.5 x ULN, or AST and ALT levels =\< 5 x ULN (for subjects with documented metastatic disease to the liver)
* Creatinine clearance \>= 30 mL/min by Cockcroft-Gault formula
* Subjects with active hepatitis B virus (Hep B) are allowed if antiviral therapy for hepatitis B has been given for \> 8 weeks and viral load is \< 100 IU/mL prior to first dose of trial treatment. Subjects with untreated hepatitis C virus (HCV) are allowed. Subjects with human immunodeficiency virus (HIV) who have CD4+ T-cell counts \>= 350 cells/uL and no history of acquired immunodeficiency syndrome (AIDS)-defining opportunistic infections in the last year are allowed
* Willingness to undergo mandatory pre-treatment biopsy (unless there is adequate archival tumor specimen available for PD-L1 IHC evaluation)
* Female subjects who are of non-reproductive potential (i.e., post-menopausal by history - no menses for \>= 1 year; OR history of hysterectomy; OR history of bilateral tubal ligation; OR history of bilateral oophorectomy). Or, female subjects of childbearing potential must have a negative serum or urine pregnancy test within 72 hours prior to the first study drug administration
* Male and female subjects who are of reproductive potential must agree to use highly effective method of birth control (e.g., implants, injectables, birth control pills with two hormones, intrauterine devices \[IUDs\], complete abstinence or sterilized partner, and female sterilization) and a barrier method (e.g., condoms, vaginal ring, sponge, etc.) during the period of therapy and for 4 months after the last dose of study drug
* Ability to understand and willingness to sign an informed consent form
* Ability to adhere to the study visit schedule and other protocol requirements
* Must be able to swallow study drug

Exclusion Criteria:

* Receiving radiation =\< 14 days prior to enrollment to the site of selected target lesions
* Systemic therapy for cancer =\< 21 days prior to enrollment
* Autoimmune disorder requiring active therapy as defined by corticosteroids at a dose \>= 10 mg oral prednisone or the equivalent or requiring chronic immunosuppressive therapy
* Use of corticosteroids =\< 14 days prior to enrollment at a dose of \>= 10 mg oral prednisone or the equivalent per day
* Received immune checkpoint inhibitor therapy (anti-PD-1, anti-PD-L1, or anti-CTLA4 directed therapy) on a prior clinical trial
* Has received selinexor or another XPO1 inhibitor previously
* Any active gastrointestinal dysfunction that could interfere with absorption of study treatment in the opinion of the investigator
* Pregnant or lactating women
* Any condition that would prohibit the understanding or rendering of informed consent
* Any condition including additional malignancies, laboratory abnormalities, or psychiatric illness that in the opinion of the investigator would interfere with the patient's safety or compliance while on trial
* Severe infection that in the opinion of the investigator would interfere with patient safety or compliance on trial within 4 weeks prior to enrollment