What property, if any, you will have to turn over to your creditors depends on several factors. First, you are entitled to certain property allowances called exemptions. Most debtors in North Carolina will be able to claim North Carolina statutory exemptions. There are several of these exemptions, but examples would include $35,000 in value for a homestead and $3,500 in value in a car. Furthermore, in a chapter 13 repayment plan, you do not have to turn over property worth more than the allowances if you pay the extra value into the plan from another source, such as future wages.
The net value of an asset to the debtor is often called the debtor's equity. For example, if a car is worth $10,000 and a car lender is owed $8,000, the debtor has $2,000 equity in the car. When the debt exceeds the value of the asset, this is referred to as "negative equity" or being "underwater".