Most times, those accounts are not used by the original owners of the accounts. They are either bought or hacked, so it will be difficult to completely stop this form of illicit activity entirely. However, I believe the secret question should be asked when old accounts that haven't been active for years try to log back in. This doesn't matter if they logged in to the account with the right password. Before they are allowed to post, they should give their answer to the secret question.
This won't eradicate the issue entirely, but accounts that were hacked won't be able to post, and it might reduce the problem.
Perhaps it would be good to apply some sort of penalty to accounts that stop interacting for a long time (years), i.e., lower their rank.
This won't make sense. People stay off the forum for a lot of reasons, it won't make sense to punish people like that simply because they were inactive for years.
Or a simple warning in their signature, on service, lending, or marketplace boards, indicating that they are interacting with an account that has been dormant for a long period of time.
This is better. It may work. It may just be there for a while and then the admins can remove it if they stay active.