If your mother was sent a social security check for benefits accrued post her death, you are not entitled to deposit or actually use the proceeds of that check since the entitlement to the social security checks ended upon her passing.If you pay out the proceeds from this social security check, the state can go after you for reimbursement of this amount. I suggest that you issue a check back to the state for the amount of the check with a letter advising that your mother has passed away. Keep a copy of all correspondence that you send for future need and reference.