Yep, they will fall off at the 7 yrs time, but your score will continue to take that hit as if it were unpaid.
As mentioned, if fully paid, a PFD won't work. A GW might work. Another option is to send a DV letter to them. Answering that letter might lead to a deletion as it is bothersome to respond. If past 7 yrs, and paid, then dispute due to CRTP. Don't call them!