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Its true that lenders like to see a paid a/c rather than unpaid. But you still would want as high a score as possible for obvious reasons and paying off a collection a/c as you are aware, would not make any difference to your score.
If the last update on your report was 2 years ago, you might actually see a small ding as the a/cs would be updated and FICO would construe that as a recent baddie.
IMO, you should try to obtain a PFD from the CA but that would in no way result in the OC deleting the a/c. You would have to send out GW requests to the OC for that. Perhaps you could also try and give PFD or PIF a shot with the OC.
Does the CA own the account?
Have you DV'd?
How are the CA 'reporting' that they 'own' the a/c? The reason for the distinction is that if the CA owns (bought) the a/c from the OC, then there is nothing you can do with the OC other than send out GW requests. The OC would be paid by the CA and hence would report a 0 balance.
If the CA has been assigned the a/c then you could still try to deal with the OC w.r.t to PIF, PFD etc.
Nope! The OC will soft you and see the unpaid CA a/c.
Did you receive the dunning letter? Is everything on your CBRs accurate? Have you DVed the CA?
Other than for promotional purposes, the OC no longer has a reason to do a soft inquiry. The FTC says once an account is paid/closed that relationship is terminated and account review inquiries should not be done.
If you are opted out, then legally I see no way they can do an inquiry of any kind.