White Button Mushroom Sup for the Reduction of PSA in Pts With Biochemically Rec or Therapy Naive Fav Risk Prostate CA

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * For therapy naive favorable risk prostate cancer (cohort 2 only): agreement to undergo baseline and 48 week prostate biopsy * Willing to forego non-study supplements containing mushroom for the duration of the study * Eastern Cooperative Oncology Group (ECOG) =\< 2 * Histologically or cytologically confirmed history of adenocarcinoma of the prostate * BIOCHEMICALLY RECURRENT PROSTATE CANCER COHORT (COHORT 1) ONLY: PSA failure defined as: * PSA of \>= 0.2 ng/mL that has increased above nadir following prostatectomy, OR * PSA increase of 2.0 ng/mL above post-therapy nadir if other primary local therapy was used instead of prostatectomy * NOTE: PSA value must be increasing based on 2 consecutive measurements taken at least 2 weeks apart * BIOCHEMICALLY RECURRENT PROSTATE CANCER COHORT (COHORT 1) ONLY: Testosterone levels \> 50 ng/dL * BIOCHEMICALLY RECURRENT PROSTATE CANCER COHORT (COHORT 1) ONLY: Received any number of primary local therapies, defined as: * Radical prostatectomy * External beam radiation therapy * Radioactive seed implantation * Cryotherapy * High-intensity focused ultrasound (HIFU) * BIOCHEMICALLY RECURRENT PROSTATE CANCER COHORT (COHORT 1) ONLY: May have received up to 24 months of neoadjuvant/adjuvant androgen deprivation therapy in conjunction with primary local therapy. Androgen deprivation therapy must have been completed \> 6 months from day (D)1 of the study * BIOCHEMICALLY RECURRENT PROSTATE CANCER COHORT (COHORT 1) ONLY: Neoadjuvant/adjuvant cytotoxic chemotherapy must have been completed \> 6 months from day (D)1 of the study * BIOCHEMICALLY RECURRENT PROSTATE CANCER COHORT (COHORT 1) ONLY: No clinical or radiographic evidence of metastatic disease within 2 months prior to day 1 of protocol therapy. If metastatic disease is detected by positron emission tomography (PET) imaging only patients are eligible as long as no metastatic disease is noted on computed tomography (CT) scan (or magnetic resonance imaging \[MRI\]) and bone scan * THERAPY NAIVE FAVORABLE RISK PROSTATE CANCER COHORT (COHORT 2) ONLY: Adenocarcinoma of the prostate diagnosed =\< 12 months of protocol screening and has elected active surveillance as preferred management plan OR already on active surveillance * THERAPY NAIVE FAVORABLE RISK PROSTATE CANCER COHORT (COHORT 2) ONLY: Clinical stage T1c-T2a as defined below: * T1c: Tumor identified by needle biopsy found in one or both sides, but not palpable * T2a: Tumor involves one-half of one side or less * THERAPY NAIVE FAVORABLE RISK PROSTATE CANCER COHORT (COHORT 2) ONLY: Gleason score =\< 6 (grade group 1) or Gleason 3+4 (grade group 2) * THERAPY NAIVE FAVORABLE RISK PROSTATE CANCER COHORT (COHORT 2) ONLY: Adequate biopsy of at least 10 biopsy cores * THERAPY NAIVE FAVORABLE RISK PROSTATE CANCER COHORT (COHORT 2) ONLY: No prior therapy for prostate cancer defined as: * Local therapy including surgery , radiation or focal therapy (cryoablation, HIFU, light) * Systemic therapy (hormonal, immunotherapy, targeted, chemotherapy). Subjects who have used 5-alpha reductase inhibitor (e.g. finasteride or dutasteride) \> 6 months prior to D1 of protocol therapy will be allowed * Platelets \> 100,000 /mm\^3 (within 28 days prior to day 1 of protocol therapy) * Hemoglobin \> 8 g/dL (within 28 days prior to day 1 of protocol therapy) * Aspartate aminotransferase, alanine aminotransferase, \< 3 x upper limit of normal (ULN) (within 28 days prior to day 1 of protocol therapy) * Total bilirubin \< 2 x ULN (within 28 days prior to day 1 of protocol therapy) * Creatinine \< 2 x ULN (within 28 days prior to day 1 of protocol therapy) Exclusion Criteria: * Other concomitant investigational anti-cancer therapy/ vaccines/biologics, corticosteroids with \> 10 mg of prednisone equivalent dose * Therapy with mushroom supplements within last 3 months of randomization * BIOCHEMICALLY RECURRENT PROSTATE CANCER COHORT (COHORT 1) ONLY: Neoadjuvant/adjuvant androgen derivation therapy lasting \> 24 months or within 6 months prior to day 1 of protocol therapy * BIOCHEMICALLY RECURRENT PROSTATE CANCER COHORT (COHORT 1) ONLY: Neoadjuvant/adjuvant chemotherapy within 6 months prior to day 1 of protocol therapy * BIOCHEMICALLY RECURRENT PROSTATE CANCER COHORT (COHORT 1) ONLY: Prior therapy for recurrent prostate cancer (unless given as a component of attempted curative salvage treatment including salvage radiation therapy, and completed \> 6 months before day 1 of protocol therapy): * Chemotherapy * Androgen deprivation therapy * Immunotherapy * Targeted therapy * Known history of allergic reaction to mushrooms * Clinically significant uncontrolled illness * Active infection requiring treatment * Uncontrolled congestive heart failure, cardiac arrhythmia * History of other primary non-skin malignancy within previous 2 years unless treated with curative intent and in remission * Any other condition that would, in the Investigator?s judgment, contraindicate the patient?s participation in the clinical study due to safety concerns with clinical study procedures * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)