Definitely not, unless they were ones the children had cosigned for or otherwise taken on. There are certainly debts that the parents estate may have to pay--for example, say that the parents owned a home worth $300k with a $200k mortgage. If the children inherit and sell the home, the mortgage has to be paid off before the children get their money.
So there are debts that the estate would have to pay and could reduce how much children might inherit. However, the children do not have to into their own pockets for any of their parents' debts.
The Answer(s) provided above are for general information only. The attorney providing the answer was not serving as the attorney for the person submitting the question or in any attorney-client relationship with such person. Laws may vary from state to state, and sometimes change. Tiny variations in the facts, or a fact not set forth in a question, often can change a legal outcome or an attorney's conclusion. Although AttorneyPages.com has verified the attorney was admitted to practice law in at least one jurisdiction, he or she may not be authorized to practice law in the jurisdiction referred to in the question, nor is he or she necessarily experienced in the area of the law involved. Unlike the information in the Answer(s) above, upon which you should NOT rely, for personal advice you can rely upon we suggest you go to AttorneyPages.com
and retain an attorney to represent you.