Phenelzine Sulfate in Treating Patients With Non-metastatic Recurrent Prostate Cancer

Inclusion Criteria: * Histologically confirmed adenocarcinoma of the prostate * Recurrent prostate cancer following primary therapy as defined by: * Post-radical prostatectomy: Any PSA \>= 0.4 ng/ml * Post-primary radiotherapy: PSA \>= 2 ng/ml above a post-radiotherapy nadir * Post-primary androgen-deprivation therapy: A confirmed rise of PSA \>= 2 ng/ml above a post-therapy nadir * For patients with non-castrate levels of circulating androgen levels (testosterone \>= 50 g/dl) * PSA levels should be increasing on at least two occasions \>= 1 week apart * Patients should not be considered candidates for radiation therapy * For patients with castrate levels of circulating androgen levels (testosterone \< 50 ng/dl): * PSA levels must be \>= 0.4 ng/ml (if history of radical prostatectomy) or \>= 2 ng/ml (if history of non-surgical primary treatment) and found to be increasing on at least two occasions \>= 1 week apart * At least 4 weeks must have elapsed since any changes to hormonal therapy, including at least 4 weeks since flutamide and at least 6 weeks since bicalutamide, nilutamide, or enzalutamide * No evidence of metastatic cancer on imaging including a bone scan and computed tomography (CT) scan of chest/abdomen/pelvis * Able to understand and adhere to dietary and medication restrictions as recommended for the safe use of phenelzine * Men with child bearing potential are required to use an effective means of contraception * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total bilirubin =\< 1.5 x upper limit of normal (ULN) except in cases of benign isolated hyperbilirubinemia such as Gilbert's syndrome. * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SPGT\]) =\< 2.5 x ULN * Creatinine =\< 1.5 x ULN Exclusion Criteria: * Uncontrolled hypertension despite appropriate medical therapy (blood pressure \[BP\] greater than 160 mmHg systolic and 90 mmHg diastolic at 2 separate measurements no more than 60 minutes apart during the screening visit); Note: patients may be rescreened after adjustment of antihypertensive medications * Known prior history of mania or major psychiatric illness (schizophrenia, bipolar disorder, severe major depression requiring hospitalization, etc.) * Concurrent use of medications contra-indicated due to potential interactions with phenelzine * Inability to comply with dietary restrictions for foods, supplements, and medications with potential for adverse interactions with phenelzine or to otherwise cooperate fully with the investigator and study personnel * History of allergic reactions attributed to compounds of similar chemical or biologic composition to phenelzine or other monoamine oxidase inhibitors * Patients may not be receiving any other investigational agents * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements