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Yes, paying a collection will yield a Paid Collection that remains for 7-1/2 years from DOFD.
Has the CA just recently contacted you?
Don't have a mortgage broker start pulling your credit report. The CA is likely monitoring your CR, and if they see "Bank of XYZ", "Mortgage Made Easy, Inc.", they'll figure they can demand the full amount and give you nothing in return.
Actually, the OC can keep selling it to another CA, and another, and another, long before 2012. That won't change the fact that they cannot report any account 7.5 years after DOFD. If the OC, CA or CRA re-ages an account by updating the DOFD, then they are in violation of the law and you can bring a lawsuit against them.
In some states, the SOL is longer than 7.5 years. As such, a CA or OC can legally bring a lawsuit even though they can no longer legally report the TL on your CR.
There is an increasing phenomenon of JDBs attempting to collect on old debts past the SOL and past the 7.5 reporting period. Even lawsuits that you might need to answer in order to avoid a default judgement.
I believe a charge off is better than a repo, but not by all that much. You would do better getting the TL deleted completely and perhaps paying more on the account. Doesn't sound like you're getting all that great of a deal from Ford.
First line of defense with CAs should always be to DV them. CAs routinely violate the FDCPA, and if you can catch them in violations that's $1,000 of leverage in your favor per violation. That leverage helps you in negotiating PFDs.