If you have been paying on a hospital debt from 2002 how long can a collection agency collect on the debt?

All debt has a statue of limitations. However that Statue of Limitations varies by locality. In most areas that Statue of Limitations is renewed whenever you make a payment. In your example the statue of Limitations is 4 years but you have been paying since 2002 and presumably have made a payment recently. In that case those 4 years begin at the time that you stop making a payment.

The short answer is that in most areas the debt is owing till its paid. If if the account is beyond the Statue of Limitations it simply means the agency can't force you to pay through court order. However, they can still request payment.

California is the notable exception but you need to research your own local laws.