Paclitaxel and Pembrolizumab in Treating Patients With Refractory Metastatic Urothelial Cancer

Inclusion Criteria: * Patients diagnosed with platinum-refractory metastatic urothelial cancer that is measureable based on Response Evaluation Criteria in Solid Tumors (RECIST) criteria 1.1.36 Platinum-refractory disease is defined as progressive disease on cisplatin or carboplatin therapy or within 12 months of prior platinum treatment (last dose.) * At least 1 prior chemotherapy regimen containing cisplatin or carboplatin * Patient must be willing to provide tissue from a newly obtained core or excisional biopsy of a tumor lesion. Newly-obtained is defined as a specimen obtained up to 6 months (168 days) prior to initiation of treatment on Day 1. Archived specimen can be used for subjects, if available * Performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) performance scale * Adequate organ function as defined below: * Absolute neutrophil count (ANC) \>= 1,500 /mcL * Platelets \>= 80,000 / mcL * Hemoglobin \>= 9 g/dL without transfusion dependency * Serum creatinine =\< 1.5 X upper limit of normal (ULN) OR measured or calculated creatinine clearance (glomerular filtration rate \[GFR\] can also be used in place of creatinine or creatinine clearance rate \[CrCl\]) \>= 35 mL/min for subject with creatinine levels \> 1.5 X institutional ULN * Serum total bilirubin =\< 1.5 X ULN OR direct bilirubin =\< ULN for subjects with total bilirubin levels \> 1.5 ULN * 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 * Albumin \>= 2.5 mg/dL * 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 * Ability to understand and the willingness to sign an Institutional Review Board (IRB)-approved informed consent document Exclusion Criteria: * Currently receiving or has had treatment with an investigational agent or used an investigational device within 4 weeks of study day 1 * Anti-cancer monoclonal antibody (mAb) within 4 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to agents administered more than 4 weeks earlier * Chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study day 1 or who 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 * Prior therapy with an anti-programmed cell death 1 (PD-1), anti-programmed cell death-ligand 1 (PD-L1), or anti-programmed cell death-ligand 2 (PD-L2) agent. Prior therapy with paclitaxel or docetaxel * Hypersensitivity to pembrolizumab, any of its excipients, paclitaxel, or any of its excipients * 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 * Known history of active TB (Bacillus tuberculosis) * 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 * 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 * 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 * Known history of, or any evidence of active, non-infectious pneumonitis * Active infection requiring systemic therapy * 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 * Known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial * Pregnancy 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 * Known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies) * Known active hepatitis B (e.g., hepatitis B virus surface antigen \[HBsAg\] reactive) or hepatitis C (e.g., hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\] is detected) * 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