Testing How the Body Responds to the Drug CBX-12 in Patients With Advanced Solid Cancers

Inclusion Criteria: * Patients must have histologically confirmed solid tumors with metastatic disease that have progressed after \>= 1 line of prior therapy * Patients must have measurable disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) version (v)1.1, with at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as \>= 20 mm (\>= 2 cm) by chest x-ray or as \>= 10 mm (\>= 1 cm) with CT scan, MRI, or calipers by clinical exam) * Patients must have a tumor site amenable to biopsy * Age \>= 18 years of age * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Absolute neutrophil count \>= 1,500/mcL * Hemoglobin \>= 9 g/L * Platelets \>= 100,000/mcL * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) * However, patients with known Gilbert disease who have serum bilirubin level of up to 3 mg/dl may be enrolled * International normalized ratio (INR) or activated partial thromboplastin time (aPTT) =\< 1.5 institutional upper limit of normal (ULN) * Aspartate aminotransferase (AST) serum glutamic oxaloacetic transaminase (SGOT)/alanine aminotransferase (ALT) serum glutamic pyruvic transaminase (SGPT) =\< 3 x institutional ULN * AST and/or ALT =\< 5 x ULN for patients with liver involvement * Potassium ≥ lower limit of normal (LLN) * Subjects may receive supplementation to meet this eligibility criteria * Magnesium ≥ LLN * Subjects may receive supplementation to meet this eligibility criteria * Ionized/corrected calcium ≥ LLN * Subjects may receive supplementation to meet this eligibility criteria * Creatinine =\< 1.5 x institutional ULN or creatinine clearance levels \>= 60 ml/min based on the Cockcroft-Gault formula * Oxygen (O2) saturation \> 90% on room air * Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial. For these patients, an HIV viral load test must be completed within 28 days prior to enrollment * For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated * Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load * Patients with treated brain metastases are eligible if follow-up brain imaging after central nervous system (CNS)-directed therapy shows no evidence of progression for \>= 1 month after treatment of the brain metastases * Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial * Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better * The effects of CBX-12 on the developing human fetus are unknown. For this reason and because biologicals conjugated to topoisomerase 1 inhibitor agents are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control or abstinence) prior to study entry and for the duration of study participation and for at least 4 months after the last dose of study drug. 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. Women should not breastfeed while taking CBX-12 and for 4 months after cessation of treatment. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of CBX-12 administration * Willingness to provide biopsy samples for research purposes * Ability to understand and the willingness to sign a written informed consent document. Legally authorized representatives may sign and give informed consent on behalf of study participants Exclusion Criteria: * Patients must have recovered from clinically-significant adverse-events of their most recent cancer immunotherapy to grade 1 or less (with the exception for alopecia or lymphopenia) * Eligibility of subjects receiving any medications or substances with the potential to affect the activity of CBX-12 or exatecan will be determined following review of their cases by the Principal Investigator * Patients who are receiving any other investigational agents * Patients taking medication known to prolong the QT interval, or receiving any medications or substances that are strong CYP3A4 or CYP1A2 inhibitors or inducers, and sensitive substrates of CYP3A or CYP2B6 with a narrow therapeutic index are ineligible, if they cannot be transferred to alternative medication. Patients on substrates of OATP1B1 and OATP1B3 should be excluded unless they can be transferred on alternative medication. Because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated medical reference. As part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product * History of allergic reactions attributed to compounds of similar chemical or biologic composition to CBX-12 (e.g., other topoisomerase I inhibitors) or the inactive ingredients in the drug product * Patients with uncontrolled intercurrent illness that would limit compliance with study requirements * Pregnant women are excluded from this study because CBX-12 is an investigational agent with unknown potential for teratogenic or abortifacient effects. For this reason, women of child-bearing potential must agree to use adequate contraception (hormonal or barrier method of birth control or abstinence) for the duration of study participation and for at least 4 months after the last dose of the study. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother and because it is not known if the agent can be excreted in human milk, breastfeeding should be discontinued while the mother is taking CBX-12 and for 4 months after cessation of treatment