Inclusion Criteria:

          -  Patients must have been assigned to S1400F

          -  Patients must have progressed during or after prior platinum-based chemotherapy;
             patients whose only prior platinum-based chemotherapy regimen was for stage I-III
             disease (i.e. patient has not received any platinum-based chemotherapy for stage IV or
             recurrent disease), disease progression on platinum-based chemotherapy must have
             occurred within one year from the last date that patient received that therapy;
             patients must have experienced disease progression during or after prior anti-PD-1 or
             anti-PD-L1 antibody monotherapy as their most recent line of treatment; prior
             PD-1/PD-L1 combination therapy is not permitted

          -  Prior exposure to CTLA-4 inhibitors (ipilimumab and tremelimumab) is not permitted;
             prior exposure to the following is allowed: attenuated vaccines, anti-EGFR agents, and
             granulocyte-macrophage colony-stimulating factor (GM-CSF)

          -  Patients must not have received nitrosoureas or mitomycin-C within 42 days prior to
             sub-study registration

          -  Patients must not have any prior documented autoimmune or inflammatory disease
             (including inflammatory bowel disease, diverticulitis with the exception of
             diverticulosis, celiac disease, irritable bowel disease; Wegner syndrome; Hashimoto
             syndrome) within 3 years prior to sub-study registration; patients with vitiligo,
             immune-mediated alopecia, Grave?s disease, or psoriasis requiring systemic treatment
             within the past 2 years are not eligible; patients with hypothyroidism (e.g. post
             Hashimoto syndrome) who are stable on hormone replacement therapy are eligible

          -  Patients must not have any history of primary immunodeficiency

          -  Patients must not have received any immunosuppressive medication within 28 days prior
             to sub-study registration and must not be planning to receive these medications while
             on protocol therapy; systemic corticosteroids must be stopped at least 24 hours prior
             to sub-study registration; however, intranasal and inhaled corticosteroids are allowed
             at any time before and during protocol therapy

          -  Patients must not have experienced a grade 3 or worse immune-related adverse event
             (irAE) (except asymptomatic nonbullous/nonexfoliative rash) or any unresolved irAE
             grade 2, nor have experienced a toxicity that led to permanent discontinuation of
             prior anti-PD-1/PD-L1 immunotherapy

          -  Patients must not have any history of organ transplant that requires use of
             immunosuppressives

          -  Patients must not have any known allergy or reaction to any component of the
             durvalumab (MEDI4736) and/or tremelimumab formulation

          -  Patients must not have clinical signs or symptoms of active tuberculosis infection

          -  Patients must not have received a live attenuated vaccination within 28 days prior to
             sub-study registration

          -  Patients must not have known human immunodeficiency virus (HIV), or a known positive
             test for hepatitis B virus surface antigen (HBV sAg), or hepatitis C virus ribonucleic
             acid (HCV antibody) indicating current acute or chronic infection; patients with a
             positive hepatitis C antibody with a negative viral load are allowed

          -  Patients must have a thyroid-stimulating hormone (TSH) with reflex free T3/free T4 (if
             TSH is out of normal range) and electrocardiogram (EKG) obtained within 7 days prior
             to sub-study registration

          -  Patients must also be offered participation in banking and in the correlative studies
             for collection and future use of specimens