Idasanutlin, Ixazomib Citrate, and Dexamethasone in Treating Patients With Relapsed Multiple Myeloma

Inclusion Criteria: * Diagnosis of multiple myeloma (MM) with deletion 17p (del17p) or monosomy 17 by fluorescence in situ hybridization (FISH) who have received at least one line of therapy * Calculated creatinine clearance (using Cockcroft-Gault equation) \>= 30 mL/min * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3.0 x upper limit of normal (ULN) * Total bilirubin =\< 1.5 x the upper limit of the normal range (ULN) * Absolute neutrophil count (ANC) \>= 1500/mm\^3 * Platelet count \>= 75,000/mm\^3 * Hemoglobin \>= 8.0 g/dL * NOTE: white blood count and platelet count criteria must be met without any transfusion or growth factor support * Patients with measurable disease defined as at least one of the following: * Serum monoclonal protein \>= 1.0 g/dL by protein electrophoresis * \> 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 * Ability to understand the purpose and risks of the study and provide signed and dated informed consent and authorization to use protected health information * Negative pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only * Willing to follow strict birth control measures as suggested below * Female patients: if they are of childbearing potential (except if postmenopausal for at least 1 year before the screening visit, OR are surgically sterile), agree to one of the following: * Practice 2 effective methods of contraception, at the same time, from the time of signing the informed consent form through 90 days after the last dose of study drug, OR * Agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject; (periodic abstinence \[eg, calendar, ovulation, symptothermal, post-ovulation methods\] and withdrawal are not acceptable methods of contraception) * Male patients: even if surgically sterilized (ie, status post-vasectomy), must agree to one of the following: * Agree to practice effective barrier contraception during the entire study treatment period and through 90 days after the last dose of study drug, OR * Agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject; (periodic abstinence \[eg, calendar, ovulation, symptothermal, post-ovulation methods\] and withdrawal are not acceptable methods of contraception) * Willing to return to enrolling institution for follow-up (during the Active Monitoring Phase of the study) * Willing to provide bone marrow and blood samples for correlative research purposes Exclusion Criteria: * Other malignancy requiring active therapy * EXCEPTIONS: Non-melanoma skin cancer, ductal carcinoma in situ (DCIS) 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 * Other co-morbidity which would interfere with patient's ability to participate in trial, 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 * Patient has \>= grade 2 peripheral neuropathy, or grade 1 with pain on clinical examination during the screening period * Major surgery =\< 14 days before study registration * All CYP2C8 inhibitors, inducers, and substrates should be discontinued \>= 7 days prior to registration; systemic treatment with CYP2C8 inhibitors (anastrozole, montelukast, quercetin, trimethoprim, gemfibrozil, rosiglitazone, pioglitazone), inducers (carbamazepine, phenytoin, rifabutin, rifampin), or substrates (amiodarone, repaglinide, rosiglitazone, sorafenib, torsemide) should be discontinued \>= 7 days prior to registration * Systemic treatment with strong inhibitors of CYP3A4 (clarithromycin, telithromycin, itraconazole, voriconazole, ketoconazole, nefazodone, posaconazole) or strong CYP3A4 inducers (rifampin, rifapentine, rifabutin, carbamazepine, phenytoin, phenobarbital, Gingko biloba, St. John's wort) are not allowed =\< 14 days before registration * Evidence of current uncontrolled cardiovascular conditions, including cardiac arrhythmias, congestive heart failure, angina, or myocardial infarction within the past 6 months; Note: prior to study entry, any electrocardiogram (ECG) abnormality at screening must be documented by the investigator as not medically relevant * Corrected QT (QTc) \> 470 milliseconds (msec) on a 12-lead ECG obtained during the Screening period * Note: If a machine reading is above this value, the ECG should be reviewed by a qualified reader and confirmed on a subsequent ECG * Known human immunodeficiency virus (HIV) positive * Known hepatitis B surface antigen-positive status, or known or suspected active hepatitis C infection * Any serious medical or psychiatric illness that could, in the investigator's opinion, potentially interfere with the completion of treatment according to this protocol * Known allergy to any of the study medications, their analogues or excipients in the various formulations * Known gastrointestinal (GI) disease or GI procedure that could interfere with the oral absorption or tolerance of ixazomib or idasanutlin including difficulty swallowing * Diarrhea \> grade 1, based on the National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) grading, or currently taking antidiarrheals * Need for ongoing therapeutic anticoagulation * Female patients who are lactating or have a positive serum pregnancy test during the screening period * Patients that have previously been treated with ixazomib, or who participated in a blinded study with ixazomib (whether treated with ixazomib or not)