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 =\< 3.0 mg/dL)
* Serum creatinine =\< 1.5 mg/dL or creatinine clearance \>= 60 mL/min
* Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 times the upper limit of normal if no liver involvement or =\< 5 times the upper limit of normal with liver involvement
* For women of child bearing potential, documented negative pregnancy test within two weeks of study entry and agreement to acceptable birth control throughout the trial starting with the screening visit through 120 days after the last dose of study medication

  * Abstinence is an acceptable method of birth control
* Male subjects with a female partner(s) of child-bearing potential must agree to use acceptable birth control throughout the trial starting with the screening visit through 120 days after the last dose of study medication
* Capability to understand and comply with the protocol requirements as and signed informed consent documents

Exclusion Criteria:

* Systemic anticancer therapy within 21 days of the first dose of study drug

  * All adverse events from prior systemic therapy must have either stabilized or returned to baseline
* Prior treatment with nivolumab or any other PD1/PDL1 checkpoint inhibitor
* Major medical conditions that might affect study participation (e.g. uncontrolled pulmonary, renal, or hepatic dysfunction, uncontrolled serious infection, cardiac disease)
* Significant cardiac history:

  * History of myocardial infarction or ischemic heart disease within 1 year before first study drug administration;
  * Uncontrolled arrhythmia;
  * History of congenital QT prolongation;
  * New York Heart Association class III or IV cardiac disease;
  * Uncontrolled hypertension: blood pressure consistently greater than 150 mm Hg systolic and 100 mm Hg diastolic in spite of antihypertensive medication
* History of hemorrhagic diarrhea, inflammatory bowel disease or active uncontrolled peptic ulcer disease; (concomitant therapy with ranitidine or its equivalent and/or omeprazole or its equivalent is acceptable); history of ileus or other significant gastrointestinal disorder known to predispose to ileus or chronic bowel hypomotility
* Subjects with untreated symptomatic central nervous system (CNS) metastases are excluded

  * Subjects are eligible if symptomatic CNS metastases are treated and subjects have neurologically returned to baseline (except for residual signs and symptoms related to CNS treatment) for at least 7 days prior to first dose of study treatment

    * Subjects must be off corticosteroids for at least 7 days prior to first dose of study treatment
* Subjects with leptomeningeal disease are excluded
* Subjects with planned radiation therapy to a target lesion will be excluded
* Radiation therapy within 14 days of the first dose of study drug
* Subjects who are pregnant or breastfeeding are excluded
* Subjects who are unable or unwilling to abide by the study protocol or cooperate fully with the investigator or designee are excluded
* Pulmonary conditions such as sarcoidosis, silicosis, idiopathic pulmonary fibrosis, or hypersensitivity pneumonitis are excluded
* Subject who have active non-infectious pneumonitis
* Subjects who have a diagnosis of immunodeficiency or are receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of study treatment
* Subjects with any active, known, or suspected autoimmune disease; subjects with type I diabetes mellitus, hypothyroidism only requiring hormone replacement, skin disorders (such as vitiligo, psoriasis, or alopecia) not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are permitted to enroll

  * Subjects with asthma that require intermittent use of bronchodilators, inhaled steroids, or local steroid injections would not be excluded from the study
  * Subjects on chronic systemic steroids for any reason would be excluded from the study; the use of topical steroids is allowable
* Any known additional malignancy (with exception of non-melanoma skin cancer, in-situ breast cancer or a malignancy diagnosed \>= 3 years ago and with no evidence of requiring active treatment)
* Patients with known active hepatitis B, or hepatitis C will be excluded
* Patients with risk factors for bowel obstruction or bowel perforation (e.g., acute diverticulitis) will be excluded
* Has any serious or uncontrolled active infection