Simply put, there are no tax consequences for debts that are discharged through a bankruptcy.
Normally the IRS treats any cancellation of debt as income. Whenever there is a cancellation of debt, the creditor usually sends an IRS Form 1099(c) to both the IRS and the person who has the debt cancelled. This cancelled debt is then considered income for tax purposes.
However, IRS Code Section 108 specifically provides that any debt that is discharged through bankruptcy is not considered income. Therefore, for most debtors there is no tax consequence for having your debts discharged through bankruptcy.
If you have filed for bankruptcy, received a discharge of debt and have then received a 1099(c), you will need to file with the IRS Form 982 (Reduction of Tax Attributes Due to Discharge of Debt) to explain to the IRS that the cancellation of debt should not be included as income because of the bankruptcy.