Nab-paclitaxel/Rituximab-coated Nanoparticle AR160 in Treating Patients With Relapsed or Refractory B-Cell Non-Hodgkin Lymphoma, LS1681 Trial

Inclusion Criteria: * Age \>= 18 years. * Histological confirmation of relapsed/refractory B-cell NHL, CD20+ * NOTE: patients with small lymphocytic lymphoma (SLL) are eligible however patients with chronic lymphocytic leukemia (CLL) are not eligible * Waldenstrom macroglobulinemia patients are not eligible; aggressive lymphoma patients who are transplant eligible must have undergone a transplant * The biopsy confirming relapse can be up to 24 weeks prior to registration as long as there is no intervening therapy * Measurable disease (at least 1 lesion of \>= 1.5 cm in one diameter) as detected by computed tomography (CT) or the CT images of the positron emission tomography (PET)/CT. Skins lesions can be used if the area is greater than or equal to 2 cm in at least one diameter and photographed with a ruler * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1, or 2 * Absolute neutrophil count (ANC) \>= 1500/mm\^3 (obtained =\< 14 days prior to registration) * Platelet count \>= 75,000/mm\^3 (obtained =\< 14 days prior to registration) * Hemoglobin \>= 8.0 g/dL (obtained =\< 14 days prior to registration) * Total bilirubin =\< 1.5 X upper limit of normal (ULN) or if total bilirubin is \> 1.5 X ULN, the direct bilirubin =\< ULN (obtained =\< 14 days prior to registration) * Alkaline phosphatase =\< 3 X ULN unless due to direct lymphoma involvement, and then =\< 5 X ULN (obtained =\< 14 days prior to registration) * Aspartate transaminase (AST) =\< 3 X ULN unless due to direct lymphoma involvement, and then =\< 5 X ULN (obtained =\< 14 days prior to registration) * Calculated creatinine clearance must be \>= 30 ml/min using the Cockcroft-Gault formula (obtained =\< 14 days prior to registration) * Life expectancy \>= 3 months * Ability to provide written informed consent * Willing to return to enrolling institution for follow-up (during the treatment phase of the study) * Willing to provide blood samples for correlative research purposes * Failed or are intolerant to 2 or more lines of established therapy or for whom no other treatment options are available in the opinion of the investigator * Negative pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only * Disease-free of prior invasive malignancies for \> 5 years prior to registration * Note: Exception of curatively-treated basal cell or squamous cell carcinoma of the skin or carcinoma in situ of the cervix Exclusion Criteria: * 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 * Active central nervous system (CNS) lymphoma or cerebrospinal fluid involvement with malignant lymphoma cells that requires therapy * 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 * 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 * Received most recent therapy =\< 4 weeks prior to registration; NOTE: use of systemic steroid therapy is allowed pretreatment * Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm * Patients with \>= 25% of the bone marrow radiated for other diseases * Other medical conditions including but not limited to: * History of liver disease such as cirrhosis, chronic active hepatitis, chronic persistent hepatitis or hepatitis B or C * Active infection requiring parenteral antibiotics * New York Heart Association class II-IV congestive heart failure (serious cardiac arrhythmia requiring medication) * Myocardial infarction or unstable angina =\< 6 months prior to registration * Congestive heart failure requiring use of ongoing maintenance therapy for life-threatening ventricular arrhythmias * Clinically significant peripheral vascular disease * History of CNS disease (e.g., primary brain tumor, vascular abnormalities, etc.), clinically significant stroke or transient ischemic attack (TIA) =\< 6 months prior to registration, seizures not controlled with standard medical therapy * Neuropathy ˃ grade 3 * Administration of strong CYP2C8 or CYP3A4 inhibitors or inducers =\< 10 days prior to registration