Trial of the Combination of Bortezomib and Clofarabine in Adults With Relapsed Solid Tumors

-INCLUSION CRITERIA 1. Patients must have: * Histologically confirmed solid tumors that have progressed on standard therapy known to prolong survival or for which no standard treatment options exist, or * histologically confirmed myelodysplastic syndrome that has progressed on standard therapy or for which no standard treatment options exist. (As of Amendment L, January 2021, the MDS cohort has been closed due to low accrual.) 2. Age greater than or equal to18 years. 3. ECOG performance status less than or equal to 2. 4. Life expectancy of greater than 3 months 5. Patients must have normal organ and marrow function as defined below: * Absolute neutrophil count: greater than or equal to 1,500/mcL for solid tumors and lymphomas only * Platelets: greater than or equal to 100,000/mcL for solid tumors and lymphomas only * Total bilirubin: less than or equal to 1.5 X institutional ULN (\<=3 x upper limit of normal in the presence of documented Gilbert's syndrome or liver metastases at baseline) * AST(SGOT)/ALT(SGPT): less than or equal to 3 X institutional upper limit of normal OR less than 5 X institutional upper limit of normal for -creatinine: ess than or equal to 1.5 X institutional ULN OR creatinine clearance greater than or equal to 60 mL/min/1.73 m2 for patients with creatinine levels \>1.5 mg/dL 6. Bortezomib and clofarabine have both been assigned to pregnancy category D by the FDA. For this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation and for at least 3 months after dosing with study drugs ceases. 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. 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 3 months after completion of study drug administration. 7. Patients must have completed any chemotherapy, radiation therapy, or biologic therapy \>= 3 weeks (or \>= 5 half-lives, whichever is shorter) prior to entering the study. Patients must be \>= 2 weeks since any prior administration of a study drug in a Phase 0 or equivalent study and be \>= 1 week from palliative radiation therapy (patients on study may be eligible for palliative radiotherapy to non-targeted lesions after 2 cycles of therapy at the PI s discretion). Patients must have recovered to eligibility levels from prior toxicity or adverse events. Treatment with bisphosphonates is permitted. 8. For patients enrolled on the expansion cohort, patients must have tumor amenable to biopsy (excisional or incision biopsies of skin or H \& N lesions under visualization) and willingness to undergo tumor biopsies. EXCLUSION CRITERIA 1. Sensory/motor neuropathy \>= Grade 2 2. QTc interval (Fridericia formula) \> 450 msec for men or \> 470 msec for women at study entry; history of congenital long QT syndrome 3. Patients who are receiving any other investigational agents. 4. Patients with active brain metastases, CNS disease, or carcinomatous meningitis are excluded from this clinical trial. Patients with treated brain metastases are eligible if follow-up brain imaging after central nervous system (CNS)-directed therapy shows no evidence of progression. 5. History of allergic reactions attributed to compounds of similar chemical or biologic composition to study drugs. Patients who have previously received either clofarabine or bortezomib will be excluded as this may affect accurate determination of the MTD. 6. Uncontrolled intercurrent illness including, but not limited to, serious untreated infection, symptomatic respiratory failure/congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. 7. Pregnant women are excluded from this study because bortezomib and clofarabine have been assigned to pregnancy category D by the FDA. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with the study drugs, breastfeeding should be discontinued prior to the first dose of study drug and women should refrain from nursing throughout the treatment period and for 3 months following the last dose of study drug. 8. HIV-positive patients on combination antiretroviral therapy are ineligible because of possible pharmacokinetic interactions with study drugs. 9. Both men and women of all races and ethnic groups are eligible for this trial.