SOL is just the time frame where they can legally collect via obtaining a judgement, it will still remain on your reports for 7 years from the date of your last activity. Since they can't legally collect they will probably be willing to settle on amount and you can possibly PFD.
New York State enacted enhanced debt collection practices regulations in 2014, codified at 23 NYCRR Part 1, which imposes restrictions on debt collectors not imposed under the federal FDCPA if the SOL has expired.
As a result, they may wish to avoid any issues of compliance in NYS by discontinuance of further communications that would have to acknowledge expiration of SOL.
Deletion of their reported collection is not required under the FDCPA or the new NYS regs.
You would need to show that, in addition to suspending collection activities, the owner also terminated their assignment of collection authority to the assigned debt collection.
Since it has apparently been five years since DOFD, my advice would be to pay the debt,and then use the NYS shortened exclusion provision of 5 years for exclusion of a paid collection.
CRA policy would then mandate deletion of the collection if the debt collector has their collection authority terminated with the debt remaining unpaid. There is no clear evidence of any such termination, so I see no basis for requiring deletion of the collection.