Phase II Trial of Sequential Consolidation With Pembrolizumab Followed by Nab-paclitaxel

Inclusion Criteria: * Be willing and able to provide written informed consent for this trial * Be greater than or equal to 18 years of age on day of signing consent * Eastern Cooperative Oncology Group Performance Status less than or equal to 1 * Histologically or cytologically confirmed confirmed stage IV (metastatic) non small cell lung cancer as defined by American Joint Committee on Cancer (AJCC). Recurrent but not metastatic disease is allowed if deemed incurable. * Has completed or scheduled to begin 4-6 cycles of platinum based induction chemotherapy that does not include a taxane * Induction may contain, but is not require to contain bevacizumab or cetuximab. * Induction with a platinum doublet plus another biologic agent will be allowed following review by the University of North Carolina principal investigator that thee is no additional risk to the subject NOTE: Evaluable disease is not required for study entry (patients with complete response or response sufficient to preclude measurable lesions are not excluded; such patients will be evaluated for progression free survival and overall survival, but not response) * Demonstrate adequate organ function (defined in protocol). All screening labs should be performed within 14 days of treatment initiation. * Recovered from all reversible toxicities related to their previous treatment (other than alopecia) less than or equal to grade 1 or baseline; exceptions to this criteria may be allowed at the discretion of the overall principal investigator for toxicities that are not expected to be exacerbated by pembrolizumab or nab paclitaxel * Patients with brain metastases may participate if they have undergone appropriate treatment for the lesion)s), are at least two weeks post treatment without evidence for post-treatment progression, have no significant neurologic symptoms, and no longer require steroids for the reason of brain metastases * Female subject of childbearing potential should have a negative urine or serum pregnancy within 72 hours prior to receiving the first dose of study medication. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Female subjects of childbearing potential should be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 120 days after the last dose of study medication. Subjects of childbearing potential are those who have not been surgically sterilized or have not been free from menses for greater than 1 year. The two birth control methods can be two barrier methods or a barrier method plus a hormonal method to prevent pregnancy. Subjects should start using birth control from study Visit 1 throughout the study period up to 120 days after the last dose of study therapy. * Male subjects should agree to use an adequate method of contraception starting with the first dose of study therapy through 120 days after the last dose of study therapy. Exclusion Criteria: * Patients with epidermal growth factor receptor (EGFR) mutations expected to be sensitive to epidermal growth factor receptor (EGFR) inhibitors and patients with Echinoderm Microtubule-Associated Protein like 4 anaplastic lymphoma kinase (EML4/ALK) translocations are excluded, unless all available FDA approved targeted therapy options have been utilized. NOTE: In contrast to the above a patient with an EGFR mutation who has been treated with a first-generation and third generation TKIs and then with four cycles of carboplatin plus pemetrexed would be eligible * Is currently participating in or has participated in a study of an investigational agent or using an investigational device within 4 weeks of the first dose treatment * Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment * Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study Day 1. Note: if subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy * Has had a prior monoclonal antibody within 4 weeks prior to study day 1 or who has not recovered from adverse events due to agents administered more than 4 weeks earlier. Exceptions to these criteria may be allowed at the discretion overall principal for toxicities that are not expected to be exacerbated by pembrolizumab or nab-paclitaxel * Has a known additional malignancy that is progressing or requires active treatment. Exceptions include basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or in situ cervical cancer that has undergone potentially curative therapy * Has an active autoimmune disease requiring systemic treatment within the past 3 months or a documented history of clinically severe autoimmune disease, or a syndrome that requires systemic steroids or immunosuppressive agents; subjects that require intermittent use of bronchodilators or local steroid injections would not be excluded from the study. Subjects with hypothyroidism stable on hormone replacement or Sjorgen's syndrome will not be excluded from the study * Has evidence of interstitial lung disease or active, non-infectious pneumonitis * Has an active infection requiring systemic therapy * Has a history or current evidence of any condition, therapy or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial * Has inadequate home environment or social support to safely complete the trial procedures * Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment * Has received prior therapy with an anti-programmed cell death-1 (PD-1) , anti-PD-L1, anti-PD-L2, anti-CD137, or anti-Cytotoxic T-lymphocyte-associated antigen-4 (CTLA-4) antibody (including ipilimumab or any other antibody or drug specifically targeting T-cell co-stimulation or checkpoint pathways * Known hypersensitivity to protein bound paclitaxel * Has received prior therapy with any taxane chemotherapy * Has a known history of Human Immunodeficiency Virus (HIV) (HIV 1/2 antibodies) * Has known active Hepatitis B or Hepatitis C * Has received a live vaccine within 30 days prior to the first dose of trial treatment * Has a history of non-infectious pneumonitis that required steroids or evidence of interstitial lung disease or current active, non-infectious pneumonitis