I have a dumb question, but please read it through

I have a bill collector who is begging me to settle. I do agree that I made the debt and therefore I need to pay it full, even if just to ease my conscience. This bill collector keeps telling me the company needs to close the account sooner rather than later, due to the “value” of money today versus in the future, among other reasons. Can they force me to settle by taking me to court? I have already paid more than the offered settlement amount. At some point, can they send me a letter saying it is settled even if I haven’t agreed to a settlement? I’m just curious.