Testing the Addition of an Experimental Medication MK-3475 (Pembrolizumab) to Usual Anti-Retroviral Medications in Patients With HIV and Cancer

Inclusion Criteria: * Histologically or cytologically proven metastatic or locally advanced tumors for which no standard therapy exists, or where standard therapy has failed, or in patients otherwise ineligible for standard therapy, or for an indication that anti-PD-1 therapy has been shown to be effective in studies in HIV-uninfected participants; disease-specific criteria will be applied for certain common cancers and cancers strongly associated with HIV; however, enrollment will not be confined to these tumors * Non-small cell lung cancer (NSCLC) * Metastatic or locally advanced disease that progressed after at least one prior therapy * Note: patients that have actionable molecular targets (e.g., epidermal growth factor receptor \[EGFR\], anaplastic lymphoma kinase \[ALK\], c-ros oncogene 1\[ROS1\] mutations) must have received (when indicated) prior appropriate targeted therapy using Food and Drug Administration (FDA)-approved agents * AIDS-related non-Hodgkin lymphoma and other non-Hodgkin lymphoma * Failed standard first-line therapy; and * Failed autologous stem cell transplant if indicated for histology (i.e diffuse large B-cell lymphoma) or autologous stem cell transplant is not feasible * Classical Hodgkin lymphoma * Relapsed or refractory de novo classical Hodgkin lymphoma having failed standard first-line therapy; and * May have failed to achieve a response or progressed after treatment with brentuximab vedotin or may be brentuximab vedotin naive but is ineligible or unable to receive brentuximab vedotin; and * May have failed to achieve a response to, progressed after, or is ineligible for autologous stem cell transplant (auto-SCT) * Hepatocellular carcinoma (HCC) * Not eligible for curative attempt resection or liver transplant * Kaposi sarcoma impacting physical and/or psychological wellbeing and not amenable to local therapy. Patients who have received prior therapy and treatment naive patients are both potentially eligible to participate. * On antiretrovival therapy (ART) with suppressed HIV viral load for \> 3 months (Note: an extended washout period is needed to avoid treatment during the period of risk for the highly toxic and often fatal "Immune Reconstitution Inflammatory Syndrome (IRIS)" * No KSHV-associated multicentric Castleman disease in past 5 years * No symptomatic pulmonary Kapsoi sarcoma (KS) or chest X-rays positive for un-evaluated abnormalities * Disease evaluable by AIDS Clinical Trial Group (ACTG) KS response criteria * CD4+ T-cell count \>= 50 cells/uL * For KS patients, the following laboratory values supersede values below: * Platelets \> lower limit of normal * Hemoglobin \> 10 g/dL * Melanoma * Unresectable or metastatic disease progression following a BRAF inhibitor if BRAF V600 positive * Note: Prior therapy with ipilimumab not required * Available pretreatment biopsy, either fresh (optimal) or archival (acceptable) * Resolution of any adverse events (AEs) from prior treatments must be resolved to baseline or grade =\< 1 at enrollment (with the exception of alopecia), neuropathy, and ototoxicity (i.e., AEs that are not expected to improve within the washout period) * On an effective combination cART regimen, generally a 3-drug regimen based on Department of Health and Human Services (DHHS) treatment guidelines * Patients must be on cART \>= 4 weeks; and * Evidence of viral suppression defined as HIV viral load \< 200 copies/mL; and * No symptomatic AEs \> grade 1 by Common Terminology Criteria for Adverse Events (CTCAE) criteria probably or definitely attributed to cART; and * No laboratory AEs noted on protocol defined screening laboratories \> grade 1 by CTCAE criteria probably or definitely attributed to cART, with exceptions noted below * Note: if cART is modified during the screening period, patients must be on an effective new regimen for \>= 2 weeks and otherwise meet eligibility criteria * Most patients have viral loads that are suppressible to \< 50 copies/mL, but about 25% of patients will occasionally have blips up to 400-500 copies/mL, which do not appear to correlate with lack of viral suppression in most studies; thus, an HIV viral load of =\< 400 copies/mL for an occasional "blip" will be allowed, if there is documentation of an HIV viral load \< 200 on the same regimen and no significant treatment interruption * CD4+ T-cell count \>= 50 cells/uL * Patients must have marrow function and organ function as defined below * Note: to remain on treatment, any abnormal lab values allowed by the PI must remain stable or improve during treatment; similar off treatment rules will be applied to all patients, except the following: the grade of any abnormal laboratory (lab) value allowed by the protocol principal investigator (PI) at enrollment will be considered the patient's baseline for potentially resuming therapy after modification/holding of therapy when off treatment criteria are applied * Leukocytes no lower limit * Absolute neutrophil count \> 500/mcL * Platelets \> 50,000/mcL * Hemoglobin \> 9 g/dL * Total bilirubin \< 1.5 X upper limit of normal (ULN); or \< 3 x institutional ULN for Gilbert's syndrome or HIV protease inhibitors; or \< 5 x ULN and direct bilirubin \< 0.7 mg/dL for patients on atazanavir containing HIV regimen * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) \< 2.5 X institutional ULN * Creatine kinase \< 5 X institutional ULN * Serum creatinine \< 2.5 X institutional ULN OR measured or calculated\* creatinine clearance (CrCl) (glomerular filtration rate \[GFR\] can also be used in place of creatinine or CrCl) \>= 30 mL/min for subject with creatinine levels \> 2.5 X institutional ULN * Creatinine clearance should be calculated per institutional standard * Thyroid stimulating hormone (TSH) within institutional limits (ie: normal); if TSH is greater or less than institutional limits patients may participate if their T4 is within normal limits (WNL); patients may be on a stable dose of replacement thyroid medication; dose adjustments are allowed if needed * Eastern Cooperative Oncology Group (ECOG) performance score of 0 to 1 * At least 2 weeks from end of chemotherapy with resolution of neutropenia to above level * At least 2 weeks from end of radiation therapy * At least 4 weeks from end of monoclonal antibody therapy * At least 2 weeks from end of targeted therapy * Female patients of childbearing potential must have a negative urine or serum pregnancy within 72 hours before 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 * Note: the effects of MK-3475 on the developing human fetus are unknown; for this reason and because anti-PD-1 agents may be teratogenic, women of child-bearing potential must agree to use 2 methods of birth control, or be surgically sterile, or abstain from heterosexual activity beginning with the screening visit and for the duration of study participation, through 120 days beyond last dose of MK-3475 administration; patients of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \> 1 year * 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 * Men treated or enrolled on this protocol must agree to use 2 adequate methods of contraception starting with the screening visit, for the duration of study participation, and through 120 days after the last dose of MK-3475 administration * No prior treatment with anti-PD-1 or anti-PD-L1 * Measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) version (v) 1.1 or other tumor-specific criteria or disease assessable by physical exam or other methods if not measurable by RECIST * Baseline tumor tissue, either fresh (preferred) or from paraffin block/unstained slides if contemporary biopsy is unsafe or not otherwise obtainable from the primary tumor site or metastatic site to be available for use on correlative studies * Age \>= 18 years * Because no dosing or adverse event data are currently available on the use of MK-3475 (pembrolizumab) in combination with cART in patients \< 18 years of age, children are excluded from this study, but will be eligible for future pediatric trials * Ability to understand and willingness to sign a written informed consent document Exclusion Criteria: * Active systemic immunosuppressive therapy * Systemic steroid therapy or steroid therapy that cannot be discontinued with more than 7 consecutive days of steroids within the prior 2 weeks * Note: the use of prednisone or equivalent \< 0.125 mg/kg/day (absolute maximum of 15 mg/day) as replacement therapy is permitted; inhaled or topical corticosteroids are permitted * Current or history of systemic autoimmune disease requiring systemic therapy * Note: the following will NOT be exclusionary: * The presence of laboratory evidence of autoimmune disease (e.g., positive antinuclear antibody \[ANA\] titer or lupus anticoagulant) without associated symptoms * Clinical evidence of vitiligo or other forms of depigmenting illness * Mild autoimmunity not impacting the function of major organs (e.g., limited psoriasis) * Grade 3 or 4 immune related toxicity associated with prior ipilimumab therapy that has not resolved to grade 0 or 1 * Cardiovascular disease that meets one of the following: congestive heart failure (New York Heart Association class III or IV), active angina pectoris, or recent myocardial infarction (within the last 6 months) * Active tuberculosis (TB) or atypical mycobacterial infection: * Patients who are undergoing systemic antibiotics for active mycobacterial infection * Patients with TB immune reconstitution syndrome (IRIS) requiring corticosteroids * Note: patients who are receiving treatment for latent tuberculosis (isonicotinylhydrazide \[INH\] or alternative) may be eligible after discussion with the protocol P.I. * Cirrhosis with Child-Pugh score of B or C * Uncontrolled hepatitis B virus (HBV) infection, defined as acute liver failure or protracted, severe course, as indicated by total bilirubin \> 3 mg/dL (or direct bilirubin \> 1.5 mg/dL), international normalized ratio \> 1.5, encephalopathy, or ascites * Note: the following will NOT be exclusionary: * A positive hepatitis B serology indicative of previous immunization (i.e., hepatitis B surface antibody \[HBsAb\] positive and hepatitis B core antibody \[HBcAb\] negative), or a fully resolved acute HBV infection * Patients with chronic HBV infection suppressed by appropriate antiretroviral therapy with activity against HBV, as outlined in DHHS guidelines * Uncontrolled hepatitis C virus (HCV) infection, defined as plasma HCV RNA detectable by PCR * Note: the following will NOT be exclusionary: * Positive HCV serology but no detectable HCV RNA, indicative of spontaneously cleared HCV infection * Patients who have been successfully treated for HCV as long as therapy for HCV has been completed * Patients who are receiving any other investigational agents for cancer * Extensive active brain disease including symptomatic brain metastases or the presence of leptomeningeal disease, and all patients with infratentorial tumors * Note: patients with brain metastasis after definitive therapy with surgery or stereotactic radiation and stable off steroids for \> 4 weeks are eligible as are patients with asymptomatic brain metastasis as long as less than 1 cm and thus deemed as not requiring therapy by the primary physician and the lesions(s) are not infratentorial * Pregnancy or nursing or unwilling to take adequate birth control during therapy * Prior organ allograft or allogeneic transplantation, if the transplanted tissue is still in place * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia * Medical or psychiatric illness or social situations that would, in the opinion of the investigator, preclude participation in the study or the ability of patients to provide informed consent for themselves * Clinically significant lung disease including known history or evidence of interstitial lung disease or chronic obstructive pulmonary disease (COPD) that requires oxygen therapy * Active non-infectious pneumonitis \>= grade 2 or history of grade 3 non-infectious pneumonitis requiring steroids within the past 12 months; or any history of grade 4 non-infectious pneumonitis * Grade 3-4 ascites or pleural effusion * Note: The following will NOT be exclusionary: A participant who is clinically stable following treatment for ascites or pleural effusion (including therapeutic thoracentesis or paracentesis) * Receipt of live vaccines within 30 days before the first dose of trial treatment and while participating in the trial; examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, chicken pox, yellow fever, seasonal flu, H1N1 flu, rabies, bacillus Calmette-Guerin (BCG), and typhoid vaccine * History of allergic reactions attributed to compounds of similar chemical or biologic composition to MK-3475 (pembrolizumab)