Rigosertib Plus Pembrolizumab in Treating Patients With Unresectable/Metastatic Melanoma Refractory to PD-1 Inhibitors

Inclusion Criteria: * Male/female participants who are at least 18 years of age on the day of signing informed consent with histologically confirmed diagnosis of unresectable or metastatic cutaneous melanoma will be enrolled in this study. * Male participants: A male participant must agree to use a contraception during the treatment period and for at least 6 days (140 hours) plus an additional 90 days (a spermatogenesis cycle) after the last dose of study treatment and refrain from donating sperm during this period. * Female participants: A female participant is eligible to participate if she is not pregnant, not breastfeeding, and at least one of the following conditions applies: * Not a woman of childbearing potential (WOCBP) OR * A WOCBP who agrees to follow the contractive guidance during the treatment period and for at least 6 days (140 hours) plus 120 days after the last treatment dose of study. * Participants must have progressed on treatment with an anti-PD-1/L1 monoclonal antibody (mAb) administered either as monotherapy or in combination with other checkpoint inhibitors or other therapies. PD-1 inhibitor treatment progression is defined by meeting the following criteria: * For patients treated with anti-PD-1/L1 mAb in the unresectable/metastatic setting: * Has received at least 2 doses of an approved anti-PD-1/L1 mAb. * Has demonstrated disease progression after anti-PD-1/L1 as defined by Immune-Modified Response Evaluation Criteria in Solid Tumors (iRECIST). The initial evidence of progressive disease (PD) is to be confirmed by a second assessment no less than 4 weeks from the date of the first documented disease progression, in the absence of rapid clinical progression. * Progressive disease has been documented within 12 weeks from the last dose of anti-PD-1/L1 mAb. * For patients treated with anti-PD-1/L1 mAb in the adjuvant setting: * Has received at least 2 doses of an approved anti-PD-1/L1 mAb. * Develops recurrent disease during active adjuvant treatment with anti-PD-1/L1 mAb, OR * Develops recurrent disease within 6 weeks of last dose of anti-PD-1/L1 mAb. * Progressive disease is determined according to iRECIST (ie, progression by Response Evaluation Criteria in Solid Tumors \[RECIST\] version \[v\]1.1 on first imaging, confirmed with repeat imaging performed at least 4 weeks later). Once disease progression is confirmed, the initial date of disease progression documentation will be considered the date of disease progression OR * The determination of clinical progression is made by the investigator. * Participants whose disease harbors BRAF V600 mutation must have been exposed to BRAF-targeted therapy, with BRAF-targeted treatment discontinued for either progressive disease or intolerable toxicity. * The participant (or legally acceptable representative if applicable) provides written informed consent for the trial. * Have measurable disease based on iRECIST. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions. * Have provided archival tumor tissue sample or newly obtained (within 3 months of enrollment) core or excisional biopsy of a tumor lesion not previously irradiated. Formalin-fixed, paraffin embedded (FFPE) tissue blocks are preferred to slides. Newly obtained biopsies are preferred to archived tissue. * Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. Evaluation of ECOG is to be performed within 7 days prior to the first dose of study intervention. * White blood cell (WBC) \>= 3,000/uL. (Laboratory values must be collected within 10 days prior to the start of study intervention \[ie, first dose of study treatment\]). * Absolute neutrophil count (ANC) \>= 1,500/uL. (Laboratory values must be collected within 10 days prior to the start of study intervention \[ie, first dose of study treatment\]). * Platelets \>= 75,000/uL. (Laboratory values must be collected within 10 days prior to the start of study intervention \[ie, first dose of study treatment\]). * Hemoglobin \>= 9 g/dL or \>= 5.6 mmol/L. (Laboratory values must be collected within 10 days prior to the start of study intervention \[ie, first dose of study treatment\]). \* Criterion must be met without erythropoietin dependency and without packed red blood cell (pRBC) transfusion within last 2 weeks. * Serum creatinine =\< 1.5 x upper limit of normal (ULN) OR measured or calculated creatinine clearance \>= 30 mL/min for subject with creatinine levels \> 1.5 x institutional ULN (glomerular filtration rate \[GFR\] can also be used in place of creatinine or creatinine clearance \[CrCl\]). (Laboratory values must be collected within 10 days prior to the start of study intervention \[ie, first dose of study treatment\]). * Serum total bilirubin =\< 1.5 X ULN OR =\< 3.0 mg/dL for patients with Gilbert syndrome. (Laboratory values must be collected within 10 days prior to the start of study intervention \[ie, first dose of study treatment\]). * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) =\< 2.5 X ULN for subjects without liver metastases OR =\< 5 X ULN for subjects with liver metastases. (Laboratory values must be collected within 10 days prior to the start of study intervention \[ie, first dose of study treatment\]). * International normalized ration (INR) OR prothrombin time (PT) =\< 1.5 x ULN unless participant is receiving anticoagulant therapy as long as PT or activated partial thromboplastin time (aPTT) is within therapeutic range of intended use of anticoagulants. (Laboratory values must be collected within 10 days prior to the start of study intervention \[ie, first dose of study treatment\]). * Activated partial thromboplastin time (aPTT) =\< 1.5 x ULN unless participant is receiving anticoagulant therapy as long as PT or aPTT is within therapeutic range of intended use of anticoagulants. (Laboratory values must be collected within 10 days prior to the start of study intervention \[ie, first dose of study treatment\]). * Urinalysis negative for hematuria with negative blood and 0 red blood cells (RBCs) (Laboratory values must be collected within 10 days prior to the start of study intervention \[ie, first dose of study treatment\]). Exclusion Criteria: * Has a diagnosis of primary uveal or mucosal melanoma. * A WOCBP who has a positive urine pregnancy test within 72 hours of the first dose of study intervention. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. In the event that 72 hours have elapsed between the screening pregnancy test and the first dose of study treatment, another pregnancy test (urine or serum) must be performed and must be negative in order for subject to start receiving study medication. Pregnancy testing will be obtained every three months while on study treatment; patients will be withdrawn from the study if pregnancy occurs. * Has received prior systemic anti-cancer therapy including investigational agents within 4 weeks (for immunotherapeutic agents) or within 2 weeks (for targeted therapeutics) prior to the first dose of study drug. If a subject has experienced adverse events (AE) from prior treatment, he/she must have recovered from all AEs to \< grade 1 or baseline. Patients with \< grade 2 neuropathy may be eligible. Patients with endocrine-related AEs \< 2 requiring treatment or physiologic steroid replacement may be eligible. * Has received prior radiotherapy within 2 weeks of the first dose of study drug. Participants must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had radiation pneumonitis. A 1-week washout is permitted for palliative radiation (=\< 2 weeks of radiotherapy) to non-central nervous system (CNS) disease. * If participant has had recent major surgery, the participant must has recovered adequately from the procedure and/or any complications from the surgery prior to the first dose of study drug. * Has received a live vaccine or live-attenuated vaccine within 30 days prior to the first dose of study drug. Administration of killed vaccines is allowed. * Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 4 weeks prior to the first dose of study drug. Participants who have entered the follow-up phase of an investigational study may participate as long as it has been 4 weeks after the last dose of the previous investigational agent. * Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of study drug. * Has a known additional malignancy that is progressing or has required active treatment within the past 2 years. Participants with non-melanoma skin cancer (eg, basal cell carcinoma of the skin, squamous cell carcinoma of the skin) or carcinoma in situ (eg, breast carcinoma, cervical cancer in situ) that have undergone potentially curative therapy are not excluded. * Subjects with untreated active central nervous system (CNS) metastases, active brain metastases or leptomeningeal metastatic foci. For the subjects with brain metastases, if they have received treatment and have no evidence of progressive disease on magnetic resonance imaging (MRI) at least 4 weeks after completion of the treatment and within 30 days prior to the first dose, they are eligible to participate in the study. * Has a history of severe hypersensitivity (\>= grade 3), specifically infusion reaction or anaphylaxis to pembrolizumab and/or any of its excipients. * Has a history of severe hypersensitivity (\>= grade 3 reactions including wheezing, rash, or hypotension) to rigosertib and/or any of its excipients (including polyethylene glycol), or anaphylaxis. * Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (eg, thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment and is allowed. * Has a history of (non-infectious) pneumonitis/interstitial lung disease that required steroids or has current pneumonitis/interstitial lung disease. * Has an active infection requiring systemic therapy. * Has a known history of hepatitis B (defined as hepatitis B surface antigen \[HBsAg\] reactive) or known active hepatitis C virus (defined as HCV ribonucleic acid \[RNA\] \[qualitative\] is detected) infection. Note: no testing for hepatitis B and hepatitis C is required unless mandated by local health authority. * Has a known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS). * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the participant's participation for the full duration of the study, or is not in the best interest of the participant 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. * Is pregnant or breastfeeding or expecting to conceive or father children within the projected duration of the study, starting with the screening visit through 120 days after the last dose of trial treatment. * Has had an allogenic tissue/solid organ transplant.