If one can't log in to their account, how do they manage to post a question?

Anonymous is correct. All they need to do is to create a brand new account and use the same Y!A name and avatar and then at face value it may look to be the "same" account.... but then on closer inspection (e.g. different points/levels, different start dates) it's not.

There have been cases of so called "zombie" accounts in the past though which were discussed on the old Y!A Suggestion Board - I remember a spammer called Makayla whose account showed as suspended but "she" was still able to carry on posting spam regardless and even boasted about doing it until staff finally found a way to shut her down.

However in principle, if you don't log into an account then as far as I know you can't post a question unless there is trickery that isn't widely known about yet.

They usually make alternate accounts/make a new one.