Can you not accept an inherited debt?

Yes, you can choose not to accept an inherited debt, but it typically depends on the laws of your jurisdiction and the specifics of the debt. If you inherit an estate that has outstanding debts, you are generally not personally liable for those debts unless you co-signed or guaranteed them. However, the estate itself must settle its debts before any assets can be distributed to heirs. If the debts exceed the estate's assets, the estate may go into probate, and you may receive nothing.