Pembrolizumab, Standard Chemotherapy, Tumor Infiltrating Lymphocytes, and High- or Low-Dose Aldesleukin in Treating Patients With Metastatic Melanoma

Inclusion Criteria: * TURNSTILE I - SCREENING: * Patients must have metastatic melanoma or stage III in-transit, subcutaneous, or regional nodal disease * Patients must have a lesion amenable to resection for the generation of TIL on MD Anderson protocol 2004-0069 * Patients must receive a magnetic resonance imaging (MRI)/computed tomography (CT)/positron emission tomography (PET) of the brain within 6 months of signing informed consent; if new central nervous system (CNS) lesions are present, patient must have definitive treatment (including surgery or radiation); principal investigator (PI) or his designee should make final determination regarding enrollment * Clinical performance status of Eastern Cooperative Oncology Group (ECOG) 0 - 1 within 30 days of signing informed consent * Patients previously treated with immunotherapy, targeted therapy, or no therapy (treatment naive) will be eligible * Patients receiving cytotoxic agents will be evaluated by the PI or his designee for eligibility suitability * Patients with a negative pregnancy test (urine or serum) must be documented within 14 days of screening for women of childbearing potential (WOCBP); a WOCBP has not undergone a hysterectomy or who has not been naturally postmenopausal for at least 12 consecutive months (i.e. who has not had menses at any time in the preceding 12 consecutive months) * TURNSTILE II - TREATMENT: * Patients must sign the treatment consent document before Turnstile II screening procedures; before the treatment starts and at each visit, the patient will be asked to complete two quality of life questionnaires; It should take about 15 minutes to complete the questionnaires (Functional Assessment of Cancer Therapy General \[FACT-G\], FACT-Melanoma); patients must fulfill all of the following criteria to be eligible for Turnstile II of the study * Patients must have adequate TIL that were previously harvested and then cryopreserved on MD Anderson Cancer Center (MDACC) protocol 2004-0069 * Patients who have had prior therapy (BRAF inhibitors, ipilimumab, anti PD-1 antibody or anti PD-L1 antibody) or treatment naive patients are eligible as long as toxicity from therapy is grade =\< 1 or at baseline * Patients must have at least one biopsiable measurable metastatic melanoma, lesion \> 1 cm and must be amenable to undergoing serial biopsies through the course of therapy; this lesion must not be documented as one of the target lesions * Patients may have central nervous system (CNS) metastases which have been treated and are radiographically stable for at least 4 weeks * Patients of both genders must practice birth control for four months after receiving the preparative regimen (lymphodepletion) and continue to practice birth control throughout the study; patients must have a documented negative pregnancy test (urine or serum) for women who have menstruated in the past 12 months and without sterilization surgery * Unless surgically sterile by bilateral tubal ligation or vasectomy of partner(s), or if the patient is post-menopausal, the patient agrees to continue to use a barrier method of contraception throughout the study such as: condom, diaphragm, hormonal, intrauterine device (IUD), or sponge plus spermicide; abstinence is an acceptable form of birth control * Pregnancy testing will be performed within 14 days of screening for women of childbearing potential (WOCBP); a WOCBP has not undergone a hysterectomy or who has not been naturally postmenopausal for at least 12 consecutive months (i.e. who has not had menses at any time in the preceding 12 consecutive months) * Clinical performance status of ECOG 0-1 within 30 days of signing informed consent * A stress cardiac test (stress thallium, stress multi-gated acquisition scan \[MUGA\], dobutamine echocardiogram or other stress test that will rule out cardiac ischemia) within 1 month of lymphodepletion * 12-lead electrocardiogram (EKG) showing no active ischemia and corrected QT (QTc) interval less than 480 msec * Pulmonary function tests (forced expiratory volume in 1 second \[FEV1\] \> 65% or forced vital capacity \[FVC\] \> 65% of predicted) within 1 month of lymphodepletion * Have measurable disease based on RECIST 1.1 and immune related response (irRC) criteria * Absolute neutrophil count (ANC) \>= 1,500 /mcL (within 10 days of treatment initiation) * Platelets \>= 100,000 /mcL (within 10 days of treatment initiation) * Hemoglobin \>= 9 g/dL or \>= 5.6 mmol/L (within 10 days of treatment initiation) * Serum creatinine OR measured or calculated creatinine clearance (glomerular filtration rate \[GFR\] can also be used in place of creatinine or creatinine clearance \[CrCl\]) =\< 1.5 X upper limit of normal (ULN) OR \>= 60 mL/min for subject with creatinine levels \> 1.5 X institutional ULN (within 10 days of treatment initiation) * Serum total bilirubin =\< 1.5 X ULN (within 10 days of treatment initiation) OR * Direct bilirubin =\< ULN for subjects with total bilirubin levels \> 1.5 ULN (within 10 days of treatment initiation) * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X ULN or =\< 5 X ULN for subjects with liver metastases (within 10 days of treatment initiation) * International normalized ratio (INR) or prothrombin time (PT)/activated partial thromboplastin time (aPTT) =\< 1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants =\< 1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants Exclusion Criteria: * TURNSTILE I - SCREENING * Active systemic infections requiring intravenous antibiotics, coagulation disorders or other major medical illnesses of the cardiovascular, respiratory or immune system; PI or his designee shall make the final determination regarding appropriateness of enrollment * Primary immunodeficiency and need for chronic steroid therapy, exception: patients on chronic physiological dose of steroid equivalent to prednisone \< 10 mg/day is allowed * Patients who are pregnant or nursing * Presence of a significant psychiatric disease, which in the opinion of the principal investigator or his designee, would prevent adequate informed consent * TURNSTILE II - TREATMENT * Is currently participating in or has participated in a study of an investigational agent or using an investigational device within 4 weeks of the first dose of treatment * Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to initiation of lymphodepletion; exception: patients on chronic physiologic dose of steroid equivalent to prednisone \< 10 mg/day is allowed * Has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to investigational or standard agents administered more than 4 weeks earlier * Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to lymphodepletion or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to a previously administered agent * Note: subjects with =\< grade 2 neuropathy, alopecia, hypophysitis stable on physiologic dose of steroid equivalent to prednisone \< 10 mg/day, hypothyroidism stable on hormone replacement are an exception to this criterion and may qualify for the study * Note: if subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy * Has a known additional malignancy that is progressing or requires active treatment; exceptions include basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or in situ cervical cancer that has undergone potentially curative therapy * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis; subjects with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to initiation of lymphodepletion * Has an active autoimmune disease requiring systemic treatment within the past 3 months or a documented history of clinically severe autoimmune disease; subjects with vitiligo or resolved childhood asthma/atopy would be an exception to this rule; subjects that require intermittent use of bronchodilators or local steroid injections would not be excluded from the study; subjects with hypothyroidism stable on hormone replacement or Sjogren's syndrome will not be excluded from the study; subjects with hypophysitis stable on physiologic dose of steroid will not be excluded from the study * Has evidence of interstitial lung disease or has a history of non-infectious pneumonitis that required steroids or current pneumonitis * Has an active infection requiring systemic therapy * 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 trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment * Has a known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies) * Has known active hepatitis B (e.g., hepatitis B virus HBsAg surface protein antigen \[HBsAg\] reactive) or hepatitis C (e.g., hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\] is detected) * Has received a live vaccine within 30 days prior to the first dose of trial treatment * Any active systemic infections requiring intravenous antibiotics, coagulation disorders or other major medical illnesses of the cardiovascular, respiratory or immune system, such as abnormal stress thallium or comparable test, myocardial infarction, cardiac arrhythmias, obstructive or restrictive pulmonary disease; PI or his designee shall make the final determination regarding appropriateness of enrollment