I live in NJ my mom is 82 years old and only has her social security check can a collection company go after her social security check being that is her only source of living expenses?

Unless they have a judgment against her, no, but suggest the cheque not be direct deposited in her bank account where it could be accessible. Cancel direct deposit and have the cheque sent directly to her home.

I think you mean "creditor". A "debtor" is someone, such as your mom, who owes someone money.

Social security pensions are exempt from garnishment, but once deposited into a bank account become commingled funds and subject to attachment. So if using direct deposit make sure it is the only deposits to the account and that the bank is aware of the source of the deposits.