Viral Therapy in Treating Patients With Relapsed or Refractory Multiple Myeloma

Inclusion Criteria: * Patient must have relapsed or refractory myeloma that fits or did fit IMWG diagnostic criteria for symptomatic myeloma (although new or worsening end-organ damage is not required to be eligible) as defined below: * Presence of ≥ 10% clonal bone marrow plasma cells * Presence of serum and/or urinary measurable monoclonal protein or light chains * Evidence of any end-organ damage criteria listed below \[at any time\] attributed to the patient's myeloma: * Hypercalcemia: Serum calcium \> 11.5 mg/dL * Renal insufficiency: Serum creatinine \> 2 mg/dL * Anemia \> 2 g/dL below the lower limit of normal or a hemoglobin value \< 10 g/dL * Bone lesions: Lytic lesions, severe osteopenia, or pathologic fractures * Subject must have measurable disease defined as any of the following: * Serum monoclonal protein \> 500 mg/dL by protein electrophoresis * \> 200 mg of monoclonal protein in the urine on 24-hour electrophoresis * Serum immunoglobulin free light chain ≥ 100 mg/L AND abnormal serum immunoglobulin kappa to lambda free light chain ratio * Patients must have received at least one prior antineoplastic therapy and must have progressed * No standard therapy is available or patient declines such options * Prior autologous and/or allogeneic transplant is permitted although transplant must have occurred greater than 90 days prior to registration * Adverse events from prior therapy must have recovered to no greater than grade 1 with the exception of grade 2 neuropathy * Prior radiation is permitted; however, at least 4 weeks must have elapsed since the completion of prior radiation therapy and patients must have recovered from all radiation-associated toxicities to no greater than grade 1 at the time of registration * Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 (Karnofsky ≥ 60%); patients with lower performance status based solely on bone pain secondary to multiple myeloma will be eligible * Life expectancy of greater than 3 months * Absolute neutrophil count (ANC) ≥ 1,000/μL * Platelet count ≥ 50,000/μL * Hemoglobin \> 8 g/dL * Total bilirubin \< 1.5 mg/dL * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 5 times the institutional upper limit of normal. * Able to understand and willing to sign a written informed consent document * Patients must be able to avoid direct contact with pregnant or nursing women, infants, and immunocompromised individuals during the five days of Reolysin treatment and for two days after * Patients must not have known immunodeficiency virus (HIV) infection or active hepatitis B or C infections * For patients with a history of congestive heart failure, systolic cardiac function must be assessed at screening and left ventricular ejection fraction (LVEF) ≥ 50% * Females of childbearing potential (FCBP) must have a negative serum or urine pregnancy test with a sensitivity of at least 50 mIU/mL prior to starting therapy and prior to beginning another course (if applicable) * FCBP and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation * The patient must be willing to comply with fertility requirements as below: * Male patients must agree to use an adequate method of contraception for the duration of the study and for 90 days afterwards * Female patients must be either postmenopausal, free from menses ≥ 2 years, surgically sterilized, willing to use two adequate barrier methods of contraception to prevent pregnancy, or agree to abstain from heterosexual activity starting with screening and for 90 days afterwards * Patients must agree not to donate blood or sperm/ova during the course of taking protocol therapy and for at least 4 weeks after stopping treatment * No patients who have had chemotherapy or radiotherapy within 4 weeks prior to entering the study * Patients may be receiving concomitant therapy with bisphosphonates and low-dose corticosteroids (e.g., prednisone up to but no more than 10 mg by mouth daily or its equivalent) for symptom management and comorbid conditions; doses of corticosteroid should be stable for at least 7 days prior to study treatment * No patients who are receiving any other investigational agents * No uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, myocardial infarction in the preceding 6 months, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study * No patients with a "currently active" second malignancy that, in the opinion of the principal investigator, will interfere with patient participation, increase patient risk, shorten survival to \< 1 year, or confound data interpretation * No POEMS syndrome * No concurrent use of complementary or alternative medicines that, in the opinion of the principal investigator, would confound the interpretation of toxicities and/or antitumor activity of the study drug