Unpaid dental fee

Mother had a dental appo. in U.S. during her visit two years ago. Now, the dental clinic sent mail saying the insurance company rejects to pay (I don't understand why they let me two years later!). The law firm representing the clinic sent mail attempting to COLLECT A DEBT. If they don't get response from me within 30 days, they assume the debt is valid.
My question:
(1) What is COLLECT A DEBT?
(2) MY mother is in China. but she may be here next year. what is the wrost kind of senario if we refuse to pay?