Mom passed away in December 2011. The nursing home sent a bill for $7,000 this past week. Should the family pay?

My mom had been in the hospital and the bill was holding a bed while she was there (hospital). Unfortunately, she passed in the hospital. There are no funds left in my mom's name.

Due to the longevity, does the son and daughter have to pay? If we do not pay, can the NH take us to collection?