Key concepts in bankruptcy include the debtor's discharge and the related "fresh start". Discharge is available in some but not all cases. For example, in a Chapter 7 case only an individual debtor (not a corporation, partnership, etcetera) can receive a discharge.
The effect of a bankruptcy discharge is to eliminate only the debtor's personal liability, not the in rem liability for a secured debt to the extent of the value of collateral. The term "in rem" essentially means "with respect to the thing itself" (for example, the collateral). For example, if a debt in the amount of $100,000 is secured by property having a value of only $80,000, the $20,000 deficiency is treated, in bankruptcy, as an unsecured claim (even though it is part of a "secured" debt). The $80,000 portion of the debt is treated as a secured claim. Assuming a discharge is granted and none of the $20,000 deficiency is paid (for example, due to insufficiency of funds), the $20,000 deficiency—the debtor's personal liability—is discharged (assuming the debt is not non-dischargeable under another Bankruptcy Code provision). The $80,000 portion of the debt is the in rem liability, and it is not discharged by the court's discharge order. This liability can presumably be satisfied by the creditor taking the asset itself. An essential concept is that when commentators say that a debt is "dischargeable", they are referring only to the debtor's personal liability on the debt. To the extent that a liability is covered by the value of collateral, the debt is not discharged.
This analysis assumes, however, that the collateral does not increase in value after commencement of the case. If the collateral increases in value and the debtor (rather than the estate) keeps the collateral (for example, where the asset is exempt or is abandoned by the trustee back to the debtor), the amount of the creditor's security interest may or may not increase. In situations where the debtor (rather than the creditor) is allowed to benefit from the increase in collateral value, the effect is called "lien stripping" or "paring down". Lien stripping is allowed only in certain cases depending on the kind of collateral and the particular chapter of the Code under which the discharge is granted.
The discharge also does not eliminate certain rights of a creditor to setoff (or "offset") certain mutual debts owed by the creditor to the debtor against certain claims of that creditor against the debtor, where both the debt owed by the creditor and the claim against the debtor arose prior to the commencement of the case.
Not every debt may be discharged under every chapter of the Code. Certain taxes owed to federal, state or local government, student loans, and child support obligations are not dischargeable. (Guaranteed student loans are potentially dischargeable, however, if the debtor prevails in a difficult-to-win adversary proceeding against the lender commenced by a complaint to determine dischargeability. Also, the debtor can petition the court for a financial hardship discharge, but the grant of such discharges is rare.)
The debtor's liability on a secured debt, such as a mortgage or mechanic's lien on a home, may be discharged. The effects of the mortgage or mechanic's lien, however, cannot be discharged in most cases if the lien affixed prior to filing. Therefore, if the debtor wishes to retain the property, the debt must usually be paid as agreed. (See also lien avoidance, reaffirmation agreement) (Note: there may be additional flexibility available in Chapter 13 for debtors dealing with oversecured collateral such as a financed auto, so long as the oversecured property is not the debtor's primary residence.)