Well, being done in executive session (i.e. behind closed doors) would be proper. If there was no written contract, then it's considered a month to month contract.
Was your community manager licensed as required under
VA ยง 54.1-2346?
If not, this could be the reason.
Was a new manager or management company hired?
If not, perhaps the Association wanted to save money and become self managed.
I could go on guessing reasons. However I wasn't involved in the process so it would be nothing but guessing. I am of the expectation that you are a friend of the individual who was dismissed and I know that you want to support that friend. Have you considered that their was a reason but the friend doesn't want to repeat the reason why due to embarrassment? Perhaps this is why the Association is being silent about the issue as well.
No matter what the reason was (or if there was no reason) you can still support your friend by being there for them. When they are ready to talk, they will. It's also possible that they never will talk about it and you will never know the real reason.
Your option, as I see it, is to gather support and get yourself and other like minded people elected to the Board. Then if you want to rehire this individual - you will be in a position to do so.
Tim