This phase I trial studies the side effects and best dose of palbociclib when given together with dexamethasone in treating participants with B-cell acute lymphoblastic leukemia that has come back after a period of improvement or does not respond to treatment. Palbociclib may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Dexamethasone is a steroid medication that is used in combination with other medications to treat B-cell acute lymphoblastic leukemia. Giving palbociclib together with dexamethasone may work better in treating patients with B-cell acute lymphoblastic leukemia.

PRIMARY OBJECTIVES:

I. To determine the dose and schedule of the combination of palbociclib and dexamethasone in patients with relapsed or refractory adult B-cell acute lymphoblastic leukemia (ALL).

ii. To determine the safety and tolerability of the combination of palbociclib and dexamethasone in patients with relapsed or refractory adult B-cell ALL.

SECONDARY OBJECTIVES:

I. To evaluate the activity of palbociclib in combination with dexamethasone in patients with relapsed or refractory B-cell ALL.

Inclusion Criteria:

• Patients must have histologic evidence of relapsed or refractory B-cell ALL
• Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status of 2 or less
• Philadelphia chromosome positive (Ph+) patients must be refractory to or intolerant of standard tyrosine kinase inhibitor therapy
• Patients must be able to consume oral medication
• Patients must have recovered to =< grade 1 or stabilized from the toxic effects of any prior chemotherapy (except alopecia)
• Creatinine clearance (CrCL) >= 60 mL/min/1.73 m^2 calculated by Cockcroft-Gault
• Total bilirubin < 1.5 x upper limit of normal (ULN)
• Negative serum or urine pregnancy test for women with child-bearing potential
• Patients must be able to sign consent and be willing and able to comply with scheduled visits, treatment plan, procedures, and laboratory testing

Exclusion Criteria:

• Patients must not have evidence of active central nervous system (CNS) disease
• Patients must not be receiving any chemotherapy agents (except hydroxyurea); intrathecal methotrexate and intrathecal cytarabine are permissible
• Patients must not be receiving growth factors (granulocyte colony-stimulating factor [G-CSF], granulocyte-macrophage colony-stimulating factor [GM-CSF]), except for erythropoietin
• Patient must not have a concurrent active malignancy for which they are receiving treatment.
• Patients with other severe concurrent disease which in the judgment of the investigator would make the patient inappropriate for entry into this study are ineligible
• Patients must not have received any investigational agents within 30 days of study entry unless they have exceeded 5 terminal half-lives of the previous study drug used for treatment
• Patients must not be pregnant or breastfeeding; pregnancy tests must be obtained for all females of child-bearing potential within 10 days prior to enrollment; males or women of childbearing potential may not participate unless they have agreed to use an effective contraceptive method (defined as hormonal contraceptives, intrauterine devices, surgical contraceptives, or condoms)
• Patients who have uncontrolled infection are not eligible; patients must have any active infections under control; fungal disease must have been adequately treated for at least 2 weeks before study entry; subjects with bacteremia must have documented negative blood cultures prior to study entry
• Patients who are candidates for allogeneic transplantation, have a suitable donor, and are willing to undergo transplantation
• Patients who are eligible for and willing to receive treatment with tisagenlecleucel.