A supplemental proceeding is a process that requires a debtor to answer questions put forth by a creditor who has obtained a judgment. Generally, the questions will pertain to assets: where do you bank, do you own a car, etc.
A creditor can order a debtor to attend a hearing and answer questions about his/her property, for the sake of discovering property of the debtor and applying that property to the judgment. This hearing would be referred to as a supplemental proceeding.
Also called Identifying the Judgment Debtor's Property. If debtor does not pay in full or make arrangements to pay their property may be seized and sold to pay the debt.