An non collectible debt is simply a debt that can not be legally collected. Simply stated, the following circumstances would make debt non collectible:

1. Already paid
2. Not yours (identity theft)
3. You know that the debt is so old that the creditor or bill collector cannot bring action against you.
4. You become indigent. (please refer to state and local laws regarding your rights)
5. Discharged in bankruptcy.

There are many circumstances where the consumer can be "judgment proof" which means that a creditor seek remedy under civil action against debtor due to special circumstances of the debtor. Being jobless, handicapped, poverty, and many other circumstances that would make it nearly impossible for the individual to pay.
Please note that just because a debt is non collectible does not mean that you are out of the woods yet. That just means that they cannot collect. They can affect your credit reports up to 7 years on negative information. Please refer to credit repair page.