The Bankruptcy Clause is Article I, § 8, cl. 4, of the U.S. Constitution. It provides that Congress shall have the power to establish "uniform Laws on the subject of Bankruptcies throughout the United States."
A primary motivation for this clause was the interest in avoiding unjust imprisonment for debt and making federal discharges in bankruptcy enforceable in every State was a primary motivation for the adoption of that provision. But it extends broader than that, covering the entire "subject of Bankruptcies."