AOL will send any court claim to your last known address or place of business. Make sure that AOL and the debt collectors have your current address.Debt collectors have to go to court to get the money. If they don't have your current address they can get a judgment using the last known (and you may not know they've done that) If they don't bother, they don't get the money but you credit rating might still be affected.
As to the debt, it depends on the contract you had. It well may be for a fixed minimum term and provide that, even if you stop the service early and tell them, AOL is entitled to the money for the full term.They calculate their business finances on that basis.If they didn't, they'd have to factor in a guesstimate of how many customers would quit early which could prove nigh on impossible if rivals start promos where they are almost giving the service away, as a lure to new customers. On the other hand, the contract might allow for cancellation as you describe, in which case you pay nothing or whatever cancellation charge it provides for. If you do indeed owe nothing under the contract tell them and any debt collector that you'll fight the claim and why.(You'd also have a defence if the service was so bad as to be below the standard contracted for, but that doesn't appear to be the case)
If you don't have a copy of your original contract (the relevant terms may be on the back of any paper bill you have) you may be able to find a copy of the AOL contract, as it now, on AOL's website, which contract will probably have the same terms now as when you signed up..