While there is no law stating that they must accept payments, If you sent them a first check with a letter stating how you will make the payments and include on the letter that cashing the check will be considered their acceptance of those terms, I would bet good money they would cash your check. Keep negotiating with them, they will accept your payments if it means that it is the only way they will get paid. I have done this myself with a few debts and it has always gone well for me.
I have a debt that originated in June 1996 and it is now July 2002, putting me past the Statute of Limitations in our state. If I wait till next July, my credit should be free and clear. If I send them the collection agreement letter to pay $1000 (the original debt is $5717.00)to try to get it off my credit this year, am I just opening myself up for more trouble? At this point they can't find me and maybe I am just being impatient. I don't want to go for the instant gratification and have them screw me for another seven years. Any thoughts?