The death of a loved one is a difficult time, and often made more complicated when the deceased left behind debts. Today's New York Times ran an article on debt collectors who specialize in collecting monies owed by the deceased. The article implies that these companies are aggressive, often making surviving loved ones believe they are responsible for the deceased's debts.
In some instances there may be liability by the survivors, for example in a marital relationship or if someone co-signed on a loan. However, you should research your rights and obligations before paying bills of a loved one who has passed.
This story also underscores the importance of doing a probate, even in small estates. The probate process involves giving notice to known and unknown (via newspaper notice) creditors, giving them a set time frame to seek repayment. Probate is the proper venue to discharge all debts owed by the deceased. Probate is not as difficult as many people fear, and it can be completed with or without the assistance of an attorney -- depending on where you live. In Dane County (Wisconsin), the probate court has all of the forms on-line.