Paclitaxel Albumin-Stabilized Nanoparticle Formulation in Treating Patients With Relapsed or Refractory Multiple Myeloma

Inclusion Criteria:

* Absolute neutrophil count \>= 500/mm\^3
* Platelet count \>= 25000/mm\^3
* Hemoglobin \>= 6 g/dL
* Total bilirubin =\< 2.5 X institutional upper limit of normal (ULN)
* Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) =\< 5 X ULN
* Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 5 X ULN
* Creatinine =\< 3 mg/dL
* Patients with relapsed or refractory myeloma who have had \>= 3 lines of prior therapy
* 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
* Ability to understand and the willingness to sign a written informed consent document
* Negative (serum) pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only; NOTE: Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately
* Willing to return to enrolling institution (Mayo Clinic in Arizona) for follow-up and all study treatments

Exclusion Criteria:

* Myelosuppressive therapy for myeloma =\< 14 days prior to registration or those who have not recovered from acute reversible adverse events due to agents administered \> 21 days earlier
* Other concurrent chemotherapy, radiotherapy, or any ancillary therapy considered investigational; NOTE: Bisphosphonates are allowed while on protocol treatment; patients may be receiving stable doses of corticosteroids with a maximum dose of 10 mg of prednisone per day if they are being given for disorders other than lymphoma such as rheumatoid arthritis, polymyalgia rheumatica or adrenal insufficiency, or asthma
* Other active malignancy =\< 3 years prior to registration; EXCEPTIONS: Non-melanotic skin cancer or carcinoma-in-situ of the cervix; NOTE: If there is a history or prior malignancy, they must not be receiving other specific treatment (i.e. other investigational therapy, anti-neoplastic therapy, etc.) for their cancer
* Any of the following:

  * Pregnant women or women of reproductive ability who are unwilling to use effective contraception
  * Nursing women - NOTE: breastfeeding should be discontinued if the mother is treated with nab-paclitaxel (Abraxane®)
  * Men who are unwilling to use a condom (even if they have undergone a prior vasectomy) while having intercourse with any woman, while taking the drug and for 28 days after stopping treatment
* Other co-morbidity which would interfere with patient's ability to participate in trial, e.g. uncontrolled infection, uncompensated heart or lung disease
* Patients with a \>= grade 2 peripheral neuropathy