Pembrolizumab and Ibrutinib in Treating Patients With Stage III-IV Melanoma That Cannot Be Removed by Surgery

Inclusion Criteria: * PRE-REGISTRATION- INCLUSION CRITERIA * Diagnosis of unresectable stage III or metastatic melanoma (stage IV) not amenable to local therapy * At least one non-nodal lesion considered measurable by Response Evaluation Criteria in Solid Tumors (RECIST) criteria (that is, a lesion whose longest diameter can be accurately measured as \>= 1.0 cm with computed tomography \[CT\] scan, CT component of a positron emission tomography \[PET\]/CT, or magnetic resonance imaging \[MRI\]) or at least one malignant lymph node is considered measurable by RECIST criteria (that is, its short axis is \>= 1.5 cm when assessed by CT scan) * NOTE: tumor lesions in a previously irradiated area are not considered measurable disease * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1, or 2 * Provide informed written consent * Patient is willing to undergo treatment and monitoring at the enrolling institution * Willing to provide tissue and blood samples for correlative research purposes * REGISTRATION- INCLUSION CRITERIA * Histologic or cytologic confirmation of unresectable stage III or metastatic melanoma (stage IV) not amenable to local therapy * Only if patient has had previous exposure to anti-PD-1 or anti-PD-L1 therapy: * Patient had disease progression on or within 6 months after anti-PD-1/anti-PD-L1 therapy in the metastatic setting OR * Patient had disease progression within 6 months after the last dose of adjuvant/neoadjuvant anti-PD-1/anti-…