Gossypol Acetic Acid With Lenalidomide and Dexamethasone in Treating Patients With Relapsed Symptomatic Multiple Myeloma

Inclusion Criteria:

* Calculated creatinine clearance (using Cockcroft-Gault equation) \>= 60 mL/min =\<14 days prior to registration
* Absolute neutrophil count (ANC) \>= 1000/mm\^3 =\<14 days prior to registration
* Platelet count \>= 75000/mm\^3 =\<14 days prior to registration
* Hemoglobin \>= 8.0 g/dL =\<14 days prior to registration
* Patient must have relapsed and symptomatic multiple myeloma
* Measurable disease of multiple myeloma as defined by at least ONE of the following:

  * Serum monoclonal protein \>= 1.0 g/dL
  * \>= 200 mg of monoclonal protein in the urine on 24 hour electrophoresis
  * Serum immunoglobulin free light chain \>= 10 mg/dL AND abnormal serum immunoglobulin kappa to lambda free light chain ratio
* Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 or 2
* Patients must have received ≥3 prior regimens for multiple myeloma
* Provide informed written consent
* Negative pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only
* Willing to return to enrolling institution for follow-up (during the active monitoring phase of the study)
* Arm A Only (Closed): Willing to provide bone marrow and blood samples for correlative research purposes

Exclusion Criteria:

* Monoclonal gammopathy of undetermined significance (MGUS) or smoldering myeloma
* Patients who received daratumumab, pomalidomide and dexamethasone as the most immediate prior line of therapy prior to trial enrollment (prior therapy with a daratumumab-based or a pomalidomide-based regimen are allowed and prior daratumumab-pomalidomide-dexamethasone is allowed so long as it was not given as the most immediate prior line of therapy prior to trial enrollment).
* Other malignancy requiring active therapy EXCEPTIONS: non-melanotic skin cancer or carcinoma-in-situ of the cervix; NOTE: if there is a history of prior malignancy, they must not be receiving other specific treatment for their cancer
* Any of the following because this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown:

  * Pregnant women
  * Nursing women
  * Men or women of childbearing potential who are unwilling to employ adequate contraception
* Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens (e.g., uncontrolled infection, uncompensated heart or lung disease)
* Other concurrent chemotherapy, radiotherapy, or any ancillary therapy considered investigational; NOTE: Bisphosphonates are considered to be supportive care rather than therapy, and are thus allowed while on protocol treatment
* Prior severe skin reaction (toxic epidermal necrosis) with immunomodulating agents
* Major surgery =\< 14 days before study registration
* Concurrent medical problems that preclude use of deep vein thrombosis (DVT) prophylaxis with lenalidomide treatment
* Evidence of current uncontrolled cardiovascular conditions, including cardiac arrhythmias, congestive heart failure, angina, or myocardial infarction =\< 6 months prior to registration
* Immunocompromised patients and patients known human immunodeficiency virus (HIV) positive and currently receiving antiretroviral therapy NOTE: Patients known to be HIV positive, but without clinical evidence of an immunocompromised state, are eligible for this trial
* 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
* Known allergy to any of the study medications, their analogues or excipients in the various formulations