Wiktionary
n. (context finance legal US English) A natural person or corporation that has filed a bankruptcy petition, but remains in possession of property upon which a creditor has a lien or similar security interest. Such a business may continue to operate its business under Chapter 11 bankruptcy protection.
Wikipedia
A debtor in possession in United States bankruptcy law is a person or corporation who has filed a bankruptcy petition, but remains in possession of property upon which a creditor has a lien or similar security interest. A corporation which continues to operate its business under Chapter 11 bankruptcy proceedings is a debtor in possession.
Under certain circumstances, the debtor in possession may be able to keep the property by paying the creditor the fair market value, as opposed to the contract price. For example, where the property is a personal vehicle which has depreciated in value since the time of the purchase, and which the debtor needs to find or continue employment to pay off his debts, the debtor may pay the creditor for the fair market value of the car to keep it.