This is a phase 2 study that will assess the investigational drug, cabozantinib, in patients with liver cancer (specifically hepatocellular carcinoma) and who had received a liver transplant as a part of curative care, but the cancer has come back (recurred). The purpose of this study is to see how useful cabozantinib is in controlling the disease of these patients.

Cabozantinib blocks the function of various proteins found on the surface of the body's cells (called receptor tyrosine kinases) that are important in the development of cancer tumors.

All participants will receive cabozantinib until they are no longer receiving benefit from the study drug or they experience an intolerable side effect.

The study has three main parts:

Screening: Participants will have test, procedures, and assessments done for safety and eligibility. Some may be done for research purposes only. Several visits may be needed to complete the screening part of the study.

Study Drug Period: During this part, participants will take the study drug as prescribed by the study doctor. While on the study drug, participants will visit the clinic about once a week for tests, procedures, and assessments for safety, eligibility, and research only purposes.

End of Study Drug Visit and Follow-up: Participants will be asked to make an End of Study Drug visit about 30 days after the last dose of study drugs for safety, eligibility, and research only purposes. After this visit, participants will continue to have follow-up visits about every 8 weeks. If participants are experiencing side effects, they will be followed weekly for about 4 weeks, then monthly until resolution or stabilization.

Inclusion Criteria:

• Have histologically or cytologically confirmed hepatocellular carcinoma that has recurred.
• Previously underwent a liver transplant as a curative treatment for hepatocellular carcinoma (HCC).
• Not amenable to curative surgery or local treatment for recurrent disease.
• Must have measurable disease.
• No prior treatment with cabozantinib. May be systemic therapy naïve or have received up to 1 line of prior therapy for advanced HCC with sorafenib or lenvatinib.
• Age ≥18 years.
• Eastern Cooperative Oncology Group (ECOG) performance status 01.
• Life expectancy of >3 months.
• Normal organ and marrow function.
• Adequate cardiac function.
• No evidence of active uncontrolled infection.
• Understand and willing to sign written informed consent document.
• Recovered from prior toxicities to < grade 1.
• Able to take oral medications.
• Agree to use effective contraceptive methods until at least 30 days (for women) and 3 months (for men) after the last administration of study medication. Serum pregnancy test should be negative.

Exclusion Criteria:

• Had systemic therapy or radiotherapy <3 weeks.
• Receiving any other investigational agents.
• With known brain metastases unless stable for >3 months.
• History of allergic reactions attributed to cabozantinib.
• Has uncontrolled, significant intercurrent or recent illness:
• Cardiovascular disorders
• Gastrointestinal (GI) disorders including those associated with a high risk of perforation or fistula formation
• Major surgery within 2 months before randomization
• Cavitating pulmonary lesion(s) or endobronchial disease (untreated)
• Lesion invading a major blood vessel
• Clinically significant bleeding risk <3 months
• Other clinically significant disorders:
• Active infection requiring systemic treatment, known infection with human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS)-related illness
• Serious non-healing wound/ulcer/bone fracture
• Malabsorption syndrome
• Uncompensated/symptomatic hypothyroidism
• Requirement for hemodialysis or peritoneal dialysis
• Pregnant women.
• Any other condition that would, in the Investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns or compliance with clinical study procedures
• Active hepatitis B or C in liver graft
• Patients with a grade >= 2 elevated liver enzymes who are suspected of cellular rejection will undergo biopsy. Patients diagnosed with cellular rejection in the biopsy sample using the Banff schema are ineligible.
• Fibrolamellar carcinoma or mixed hepatocellular cholangiocarcinoma
• Moderate or severe ascites
• Concomitant use of anticoagulants at therapeutic doses
• Has a known history of prior invasive malignancy except if patient has undergone curative-intent therapy with no evidence of disease recurrence for 2 years prior to study entry.