Inclusion Criteria:
* Patients must have histologically confirmed cancer for which standard-of-care curative measures are no longer effective or be intolerant to those agents. Patients in cohort 1 must have colorectal cancer. Patients in cohort 2 must have pancreatic cancer. Patients in cohort 3 may have any of the following cancers:
* Biliary
* Gastroesophageal
* Urothelial
* Ovarian
* Non-small cell lung (adenocarcinoma only)
* Patients must have measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) v1.1 disease.
* Patients must have radiographic documentation of metastatic disease with imaging within =\< 6 weeks prior to registration.
* Patients must be age \>= 18 years.
* Patients must exhibit an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. Performance Status of 2 will be allowed with approval from principle investigator (PI) on a case-by case basis.
* Note: Performance status of 2 will be allowed with approval from PI on a case-by case basis. Documentation of PI approval in these cases will be stored with inclusion/exclusion signed checklist for patient and/or in patient's shadow chart.
* Patients must have exhausted all available molecularly targeted therapies (e.g., anti-PD-1/anti-PD-L1 agents where indicated).
* Absolute neutrophil count (ANC) \>= 1,500/mcL (within the last 14 days of screening)
* Hemoglobin (Hgb) \>= 9 g/dL (within the last 14 days of screening) (Transfusions permitted. Eligibility labs should be drawn \>= 7 days from transfusion).
* Platelets (PLT) \>= 100,000/mcL (within the last 14 days of screening) (Transfusions permitted. Eligibility labs should be drawn \>= 7 days from transfusion).
* INR (international normalized ratio) =\< 1.6 (within the last 14 days of screening) (unless receiving anticoagulation therapy) If receiving anticoagulant: INR =\< 3.0 and no active bleeding, (i.e., no bleeding within 14 days prior to first dose of study therapy).
* Total bilirubin =\<1.5 x Institutional upper limit of normal (ULN) (within the last 14 days of screening)
* Note: Patients with Gilbert's Syndrome are exempt. Patients with liver metastases with no significant bilirubin obstruction may have a total bilirubin level of =\< 2.0 mg/dL.
* Aspartate aminotransferase (AST) serum glutamic-oxaloacetic transaminase (SGOT) =\< 2.5 x institutional ULN (within the last 14 days of screening)
* Note: If liver metastases are present, then =\< 5 x ULN is allowed.
* Alanine transaminase (ALT) serum glutamic-pyruvic transaminase (SGPT) =\< 2.5 x institutional ULN (within the last 14 days of screening)
* Note: If liver metastases are present, then =\< 5 x ULN is allowed.
* Serum albumin \> 3.0 g/dL (within the last 14 days of screening)
* Creatinine =\< 1.5 x ULN OR glomerular filtration rate (GFR) \>= 50 mL/min/1.73 m\^2 (within the last 14 days of screening)
* eGFR is estimated GFR calculated by the abbreviated Modification of Diet in Renal Disease (MDRD) equation
* The effects of combination treatment of CPI-613, 5-FU, gemcitabine, and HCQ on the developing human fetus are unknown. For this reason and because antineoplastic agents as well as other therapeutic agents used in this trial are known to be teratogenic, patients of child-bearing potential (POCBP) regardless of gender must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) from time of informed consent, for the duration of study participation, and for 180 days following completion of therapy. Patients who can impregnate their partners regardless of gender must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) from time of informed consent, for the duration of study participation, and for 180 days following completion of therapy. Should a patient become pregnant or suspect they are pregnant while they or their partner is participating in this study, they should inform their treating physician immediately.
* Note: At the discretion of the investigator, acceptable methods of contraception may include total abstinence in cases where the lifestyle of the patient ensures compliance. (Periodic abstinence \[e.g., calendar, ovulation, symptothermal, postovulation methods\] and withdrawal are not acceptable methods of contraception.)
* Note: A POCBP is any person with an egg-producing reproductive tract (regardless of sexual orientation, having undergone a tubal ligation, or remaining celibate by choice) who meets the following criteria:
* Has not undergone a hysterectomy or bilateral oophorectomy
* Has had menses at any time in the preceding 12 consecutive months (and therefore has not been naturally postmenopausal for \> 12 months)
* POCBP must have a negative pregnancy test prior to registration on study.
* Note: If negative pregnancy test result is \>7 days from first dose of study treatment it must be repeated at time of first dose of study treatment (with any of the four drugs used in this study).
* For patients with a known history of human immunodeficiency virus (HIV), infected patients on effective anti-retroviral therapy must have a viral load undetectable for 6 months prior to registration.
* For patients with a known history of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated.
* Patients with a known history of hepatitis C virus (HCV) infection must have been treated and cured. Patients with HCV infection who are currently on treatment, must have an undetectable HCV viral load. Patients with known history or current symptoms of cardiac disease, or history of treatment with cardio toxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. Patients must be class 2B or better.
* Note: Patients with pacemakers where corrected QT interval (QTc) is not a reliable measure will require an evaluation by a cardiologist to exclude co-existing cardiac conditions which would prohibit safe participation in the study.
* Patients must have the ability to understand and the willingness to sign a written informed consent document for the duration of the entirety of the study.
* Patients must be reliable, willing to make themselves available for the duration of the entire study and willing to follow screening procedures.
Exclusion Criteria:
* Patients who have not recovered from adverse events due to prior anti-cancer therapy (i.e., have residual toxicities \> grade 1).
* Note: Patients who experience adverse events of alopecia and peripheral neuropathy that have not recovered are eligible; patients with any lab abnormality that is above grade 1 related to previous therapy found to be not clinically significant will also be eligible.
* Patients with symptomatic brain metastases currently using corticosteroids.
* Note: Patients with brain metastases who are asymptomatic and off corticosteroids for at least one week are eligible.
* Patients with severe obstructive pulmonary disease or interstitial lung disease.
* Patients with a history of myocardial infarction that is \<90 days prior to registration.
* Patients using concomitant medications that prolong the QT/QTc intervals. For example, patients receiving amiodarone. Using amiodarone together with hydroxychloroquine can increase the risk of long QT syndrome that although rare, may be serious, and potentially life-threatening.
* Patients with a history of additional risk factors for drug-induced QT prolongation or Torsades de Pointes (TdP) (e.g., heart failure, hypokalemia, family history of long QT syndrome).
* Patients with major surgery or significant traumatic injury =\< 21 days prior to registration.
* Patients receiving treatment with low dose chemotherapy concurrent with radiation =\< 21 days prior to registration.
OR patients who have had chemotherapy or radiotherapy =\< 21 days (42 days for nitrosoureas or mitomycin C) prior to registration.
* Note: Palliative radiation before and during study participation is permissible providing it is not to a target lesion.
* Patients who have an uncontrolled intercurrent illness including, but not limited to any of the following, are not eligible:
* Ongoing or active infection requiring systemic treatment.
* Clinically significant complications such as perforation, gastrointestinal bleeding, or diverticulitis within 42 days prior to registration.
* Symptomatic congestive heart failure; symptomatic coronary artery disease, symptomatic angina pectoris, or symptomatic myocardial infarction.
* Unstable angina pectoris.
* Unstable cardiac arrhythmia.
* Psychiatric illness/social situations that would limit compliance with study requirements.
* Active substance abuse.
* Any other illness or condition that the treating investigator feels would interfere with study compliance or would compromise the patient's safety or study endpoints.
* Patients who are pregnant or nursing.
* Patients with Fridericia-corrected QT interval (QTcF) \> 470 msec (female) or \> 450 (male), or history of congenital long QT syndrome. Any electrocardiogram (ECG) abnormality that in the opinion of the investigator would preclude safe participation in the study.
* Patients who have pre-existing retinopathy of the eye.
* Patients who are unable to swallow or retain and absorb oral medication
* Patients with known hypersensitivity to any of the following: CPI or its inactive components, 4-aminoquinoline compounds, or quinine.
* Patients with poorly controlled diabetes mellitus (glycosylated hemoglobin (HbA1c) of \> 7%, pre-prandial capillary plasma glucose \> 130mg/dl, and peak postprandial capillary plasma glucose of \> 180mg/dl).
Active drug
