Nivolumab and Plinabulin in Treating Patients With Stage IIIB-IV, Recurrent, or Metastatic Non-small Cell Lung Cancer

Inclusion Criteria: * Subjects must have histologically or cytologically-documented stage IIIB or stage IV, recurrent, or metastatic non-small cell lung cancer (NSCLC) * Subjects must have received prior platinum doublet based treatment * Up to 2 lines of prior systemic therapy for metastatic disease are permitted * Adjuvant chemotherapy or concurrent chemoradiation for early stage disease does not count as prior therapy unless subject progressed within 6 months of completion of regimen * Patients with known activating mutations in epidermal growth factor receptor (EGFR), or known translocation in anaplastic lymphoma kinase (ALK) or ROS-1 are eligible provided they have progressed on or were intolerant to Food and Drug Administration (FDA) approved targeted therapy * Subjects must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2 * Subjects, including those in the dose-escalation portion of the study, must have measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria; imagining must be within 28 days of trial enrollment * Target lesions may be located in a previously irradiated field if there is documented (radiographic) disease progression in that site prior to trial enrollment * Absolute neutrophil count (ANC) \>= 1000/mm\^3 * Platelets \>= 75,000/dL * Hemoglobin \>= 9 g/dL * Total bilirubin =\< 1.5 mg/dL x upper limit of normal (ULN) (except subjects with Gilbert syndrome who can have total bilirubin …