Propranolol Hydrochloride and Pembrolizumab in Treating Patients With Stage IIIC-IV Melanoma That Cannot Be Removed by Surgery

Inclusion Criteria: * Participants must be newly diagnosed, treatment-naive with histologically confirmed stage IIIC unresectable melanoma or stage IV melanoma * Have an Eastern Cooperative Oncology Group (ECOG) performance status 0-1 * Available archival formalin-fixed paraffin-embedded (FFPE) from a prior biopsy or, participant must be willing to have a tissue biopsy taken at a clinic visit prior to start of study treatment * Have measurable disease per irRECIST v1.1 * Ability to swallow and retain oral medication * Absolute neutrophil count (ANC) \>= 1500/uL * Hemoglobin (Hb) \>= 9 g/dL * Platelet count \>= 100, 000/uL * Total bilirubin =\< 1.5 x ULN (upper limit of normal) - unless patient has Gilbert's syndrome * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2 x ULN * If the patient has liver metastasis AST and ALT less than or greater to 5x ULN * Serum or plasma (based on site's SOP) creatinine \< 2 x ULN * Participants of child-bearing potential must have a negative pregnancy test at study entry and then agree to use adequate contraceptive methods (e.g., hormonal or barrier method of birth control; abstinence) prior to study entry; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately * Participant must understand the investigational nature of this study and sign an Independent Ethics Committee/Institutional Review Board approved …