Testing Interruption of Hormonal Medications in Patients Responding Exceptionally to Therapy for Metastatic Prostate Cancer, (A-DREAM)

Inclusion Criteria: * Histologic or clinical diagnosis of metastatic prostate cancer * Must have had evidence of metastatic disease by bone scan; or bone, nodal or visceral lesions on CT or MRI prior to starting on intense antiandrogen therapy (ADT) * If only positron emission tomography (PET) imaging was performed prior to starting on intense ADT, then there must have been evidence of metastatic disease on the CT/MRI component (i.e. sclerotic bone lesion, non-regional lymph node \>= 15 mm, and/or soft tissue lesion \>= 10 mm). * Radiographic evidence of disease is not required at the time of enrollment * No metastases to liver or to brain, as these represent aggressive variant disease biology for which intermittent treatment may not be favored * Must currently be receiving intense ADT for metastatic hormone sensitive prostate cancer (mHSPC) * Testosterone suppression (TS) with luteinizing hormone releasing hormone (LHRH)-agonist or LHRH-antagonist AND * An approved secondary androgen receptor pathway inhibitor (ARPI) abiraterone, enzalutamide, apalutamide or darolutamide) * Must have remained on testosterone suppression for metastatic disease continuously (without treatment breaks) for 540-750 days (approximately 18 to 24 months) from time of first dose of LHRH agonist or antagonist by time of registration. A period of anti-androgen treatment prior to LHRH agonist or antagonist initiation is not included in the 540 - 750 days (approximately 18 to 24 months) * Must have received treatment with ARPI for at least 360 days in total by time of A032101 registration. Treatment breaks from the ARPI of up to 60 days are permitted (for example peri-procedural or for management of a temporary adverse event or lapse in financial coverage) as long as PSA did not rise while holding therapy and the patient has resumed for at least 30 days (without a dose hold \> 72 hours within those 30 days) by time of registration. A break from ARPI longer than 60 days is permitted if a patient needed to discontinue a different ARPI for toxicity, as long as PSA did not rise while holding therapy and the patient has received at least 360 days of ARPI in total. * Prior TS in the context of neoadjuvant/concurrent/adjuvant treatment with local therapy is permitted. Prior course(s) of intermittent TS for biochemical-only recurrence is permitted. However, if the patient previously received TS, metastatic progression for which intense ADT was initiated must have occurred during an off-treatment interval and with testosterone \>= 150 ng/dL * Prior local therapy for prostate cancer (either before or after diagnosis of metastatic disease) is permitted. Prior treatment with docetaxel chemotherapy for up to 6 cycles is permitted. Prior radiation therapy to metastatic sites (either for symptom palliation or for ablation of oligometastatic disease) is permitted Exclusion Criteria: * No history of surgical castration * No history of ARPI use prior to diagnosis of mHSPC for which the patient is currently receiving intense ADT (such as in the neoadjuvant setting with prior local therapy) * No current or prior treatment with experimental agents for metastatic hormone-sensitive prostate cancer * Eastern Cooperative Oncology Group (ECOG) performance status 0-2 * Prior to initiating intense ADT * PSA \>= 5 ng/ml (does not need to be the most recent value prior to enrollment) * Testosterone \>= 150 ng/dl. Patients are permitted to enroll if testosterone was not measured prior to initiating intense ADT for mHSPC if they did not previously receive TS and were not known or suspected to be hypogonadal at the time * At time of enrollment to A032101 * PSA \< 0.2 ng/ml \*\* PSA values (measured in the same laboratory) must be stable or falling for 3 consecutive measurements - i.e. any PSA rise must be followed by a decrease in PSA that is further decreased or stable on a 3rd measurement. Any patient with 2 consecutive rises in PSA values since achieving castrate level of testosterone is not eligible * Testosterone \< 50 ng/dl * No current participation in a clinical study that does not allow for TS or ARPI interruption * No patients with a "currently active" second malignancy \* Patients with non-melanomatous skin cancer, superficial bladder cancer, cancer not needing active therapy for at least 2 years, cancer for which the treating investigator deems the subject