Testing Nivolumab and BMS-986016 (Relatlimab) as Potentially Targeting Treatment in Cancers That Are LAG-3+ and Have Mismatch Repair Deficiency (MATCH - Subprotocol Z1M)

Inclusion Criteria: * Patients must have met applicable eligibility criteria in the Master MATCH Protocol EAY131/ NCI-2015-00054 prior to registration to treatment subprotocol * Patients must fulfill all eligibility criteria of MATCH Master Protocol at the time of registration to treatment step (Step 1, 3, 5, 7) * Patients must have mismatch repair deficiency based on one of the following: * Mismatch repair testing done in any laboratory under Clinical Laboratory Improvement Act (CLIA) conditions with immunohistochemistry (IHC) for MLH1/MSH2 +/-MSH6 +/-PMS2 OR * Polymerase chain reaction (PCR)-based microsatellite testing using a validated assay done in any laboratory under CLIA conditions OR * A MATCH designated laboratory determination of mismatch repair (MMR) status by deoxyribonucleic acid (DNA) sequencing * Patients must have LAG-3 expression at \>= 1% as determined via the MATCH Master Protocol * NOTE: For patients entering the study, all patients must have LAG-3 testing performed as described in the MATCH Master Protocol. This includes patients entering the study via the outside assay process * Patients with active melanoma are ineligible * Patients must have an electrocardiogram (ECG) within 8 weeks prior to treatment assignment and must have no clinically important abnormalities in rhythm, conduction or morphology of resting ECG (e.g. complete left bundle branch block, third degree heart block) * Patients must have Troponin T (TnT) or I (TnI) \< 2 x upper …