Facebook – Creating an Application on Facebook

From a technological perspective, the important problem which you are addressing -- that of a disgruntled admin "hijacking" a Facebook application -- does not seem to currently have a solution.

This problem is virtually identical to that of a Facebook page being similarly hijacked, and as mentioned in this article on Mashable from Sept. 2011, the latter seems to be a flaw in Facebook's security architecture. Judging from the articles found in a Google search today for "hijack facebook page disgruntled employee", it would seem that this flaw has not yet been fixed.

Moreover, technologically, this danger exists regardless of the legal nature of the business entity involved. So, I don't think that the perspective of an LLC changes anything.

From your description of the "repeating cycle," I suspect that you were not asking for a legal perspective on how to prevent or manage this problem, say, via clauses in contracts ... etc.

Facebook only allows accounts that belong to a person to create apps. They do not value a company page as an account that is supposed to anything but promoting themselves. The people behind (which usually are admins) can create apps.