Each state has different statute of limitations in which the vendor can collect on their debt. Texas, for example is 4 years, so if the debt was from 2001, he would no longer be required to pay. The vendor may or may not continue to pursue the debt, but again, your DH would not be required to pay.
Paying off a debt that has been "charged off" will remove the balance owed, but it will still be reflected as "charged off" on your credit report. This is still harmful when applying for a loan/c.c. so some people don't bother paying it off. When applying for a mortgage, however, they will often require any charge offs to be paid off in full.