To reassign debt is to transfer debt back to the original creditor. In the US, debt is often sold as an asset (of sorts) and the legal interest in the debt can be exchanged between various companies. For example, if you owe a credit card company $2,000 the company can assign the debt to a collection agency; you would then not owe the credit card company anything but would instead owe $2,000 to the collection agency.
At some future point, the collection agency might reassign the debt to the credit card company. This process is commonly used to move debt around various departments inside a large company.