Testing the Role of DNA Released From Tumor Cells Into the Blood in Guiding the Use of Immunotherapy After Surgical Removal of the Bladder, Kidney, Ureter, and Urethra for Urothelial Cancer Treatment, MODERN Study

Inclusion Criteria: * PRE-REGISTRATION (STEP 0): Histologically confirmed muscle-invasive urothelial carcinoma of the urethra, bladder, ureter or renal pelvis * PRE-REGISTRATION (STEP 0): Variant histology, including neuroendocrine differentiation, sarcomatoid, micropapillary, glandular, trophoblastic, Mullerian, is allowed if urothelial cancer is predominant histology (any amount of squamous differentiation is allowed provided the tumor is not a pure squamous cell cancer) * PRE-REGISTRATION (STEP 0): Radical surgery (cystectomy with lymph node dissection or nephroureterectomy or ureterectomy) must be ≥ 3 weeks and ≤ 12 weeks (central Signatera pathway) or ≤ 16 weeks (commercial Signatera pathwary) prior to pre-registration. Patients who have had a partial cystectomy as definitive therapy are not eligible * PRE-REGISTRATION (STEP 0): Patients who have had a partial cystectomy as definitive therapy are not eligible * PRE-REGISTRATION (STEP 0): No gross cancer at the surgical margins. Microscopic invasive urothelial carcinoma at the surgical margins (i.e., "positive margins") are allowed. Carcinoma in situ (CIS) at margins is considered negative margins * PRE-REGISTRATION (STEP 0): No evidence of residual cancer or metastasis after radical cystectomy or nephroureterectomy or ureterectomy (imaging is not required prior to pre-registration but is required prior to registration) * PRE-REGISTRATION (STEP 0): Have undergone a radical cystectomy nephroureterectomy, or ureterectomy with pathological evidence of urothelial carcinoma at high risk of recurrence as described in one of the two scenarios below (i or ii). The 7th edition of American Joint Committee on Cancer (AJCC) staging will be utilized.: * (i) Patients who have not received neoadjuvant systemic therapy: pT4N0 or pTanyN+ on radical surgery pathology specimen (i.e., cystectomy, nephroureterectomy, or ureterectomy) and are not eligible for adjuvant cisplatin chemotherapy * (i) Patients ineligible for cisplatin due to at least one of the following criteria and reason for ineligibility should be documented: * (i) Creatinine Clearance (using Cockcroft-Gault): \< 60 mL/min * (i) Common Terminology Criteria for Adverse Events (CTCAE) version 5, grade \>= 2 audiometric hearing loss * (i) CTCAE version 5, grade \>= 2 or above peripheral neuropathy * New York Heart Association Class III heart failure * (i) Eastern Cooperative Oncology Group (ECOG) performance status = 2 * (i) Patients who are eligible for adjuvant cisplatin may be candidates if they refuse adjuvant cisplatin-based chemotherapy, despite being informed by the investigator about the treatment options. The patient's refusal must be documented. * (i) Patients with pT2N0 urothelial cancer on radical surgery specimen (without prior neoadjuvant systemic therapy) with ctDNA(+) Signatera results are eligible only if the result was obtained via commercial testing (central testing is not permitted for this population) (Note: this is distinct from patients with ypT2N0 who are eligible based on ii). * (ii) Patients who received neoadjuvant systemic therapy: ypT2-T4N0 or Nx or ypTanyN+ on radical surgery (i.e., cystectomy. , nephroureterectomy, or ureterectomy) pathology specimen. Neoadjuvant systemic therapy may have included cisplatin-based chemotherapy, cisplatin-based chemotherapy plus PD-1/PD-L1 blockade, or enfortumab vedotin plus PD-1/PD-L1 blockade * PRE-REGISTRATION (STEP 0): Patients are required to meet criteria for one of two criteria: * 1\) Commercial Signatera pathway: * Available commercial Signatera testing result (i.e., ctDNA+ or ctDNA-) from blood sample obtained ≥ 3 weeks and ≤ 16 weeks from time of radical surgery performed as part of standard care * Sites are required to verify that the commercial Signatera report demonstrates a complete 16 target assay design and that the test was designed on exome. This verification is conducted at the site level during the eligibility review. OR * Central Signatera pathway: * Pre-registration samples are to be submitted after pre-registration, at ≥ 3 weeks but ≤ 12 weeks from the time of radical surgery * Ineligible patients for the commercial pathway must use the central Signatera pathway and provide tumor tissue as part of the A032103 study * For patients who have not had neoadjuvant chemotherapy, tumor tissue is preferred from the radical surgery specimen * For patients who have had neoadjuvant therapy, tissue is preferred from the pre-chemotherapy specimen diagnosing muscle-invasive disease (e.g., transurethral resection of bladder tumor specimen) * PRE-REGISTRATION (STEP 0): Age \>= 18 years * PRE-REGISTRATION (STEP 0): ECOG performance status 0-2 * PRE-REGISTRATION (STEP 0): Not pregnant and not nursing, because this study involves an agent that has known genotoxic, mutagenic and teratogenic effects * PRE-REGISTRATION (STEP 0): No postoperative adjuvant systemic therapy after radical surgery * PRE-REGISTRATION (STEP 0): No adjuvant radiation after radical surgery * PRE-REGISTRATION (STEP 0): No treatment with any other type of investigational agent =\< 4 weeks before pre-registration * PRE-REGISTRATION (STEP 0): No previous treatment with LAG-3 blockade therapy * PRE-REGISTRATION (STEP 0): Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial * PRE-REGISTRATION (STEP 0): Absolute neutrophil count (ANC) \>= 1,200/mm\^3 * PRE-REGISTRATION (STEP 0): Platelet count \>= 100,000/mm\^3 * PRE-REGISTRATION (STEP 0): Hemoglobin \>= 8 g/dL * PRE-REGISTRATION (STEP 0): Creatinine =\< 1.5 x upper limit of normal (ULN) or calculated (calc.) creatinine clearance \> 30 mL/min (using either Cockcroft-Gault formula or Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation * PR