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 written informed consent form prior to receiving any study related procedure Exclusion Criteria: * Participants who have received previous immunotherapy for any cancer (excluding melanoma) including PD-1/PD-L1 inhibitors but not interferons and CTLA-4 inhibitors * Participants with chronic autoimmune diseases * Participants that are already on non-selective B-AR blockers for various indications. Patients on selective beta-blockers are considered eligible for enrollment with a caveat that their clinician prescribing the beta-blocker is willing to discontinue their selective beta-blocker in order to transition to propranolol at the specified protocol dose. * Participants with symptomatic known brain metastases \< 4 weeks from radiation treatment should be excluded from this clinical trial * Other invasive cancers diagnosed \< 3 years back that required systemic treatment. If diagnosed with other invasive cancer \>=3 years, should have complete recovery from all systemic toxicity except neuropathy and alopecia * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant or nursing female participants, where pregnancy is defined as the state of a female after conception and until the termination of gestation, confirmed by a positive human chorionic gonadotropin (hCG) laboratory test * Unwilling or unable to follow protocol requirements * Any condition which in the investigator's opinion deems the participant an unsuitable candidate to receive study drug * Other active non-melanoma metastatic cancers * Contraindications to the use of beta-blockers, like, uncontrolled depression, unstable angina pectoris, uncontrolled heart failure (grade III or IV), hypotension (systolic blood pressure \< 100 mmHg), bradycardia (resting heart rate \<55bpm), severe asthma or chronic obstructive pulmonary disease (COPD), uncontrolled type I or type II diabetes mellitus (glycosylated hemoglobin \[HbA1C\] \> 8.5 or fasting plasma glucose \> 160 mg/dl at screening), symptomatic peripheral arterial disease or Raynaud's syndrome, untreated pheochromocytoma, current use or past use in the last two years of non-selective beta-blockers or non-dihydropyridine calcium channel blockers. Patients on selective beta blockers will be eligible for enrollment only under the condition that their prescribing clinician is willing to discontinue their selective beta blocker in order to begin propranolol and only at the specified dose (after which time the patient is not to be started on any non-selective beta-blockers or non-dihydropyridine calcium channel blockers) * Patient is currently receiving or has received systemic corticosteroids (=\< 2 weeks prior to starting study drug, or who have not fully recovered from side effects of such treatment) * Diagnosis of immunodeficiency or receiving systemic steroid therapy or any other form of immunosuppressive therapy within 14 days prior to the first dose of the study drug * Has received a live vaccine or live-attenuated vaccine within 30 days prior to the first dose of trial treatment and while participating in the trial. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster, yellow fever, rabies, BCG, and typhoid vaccine. Administration of killed vaccines is allowed.