Legal Question in Elder Law in California

In order to have a cause of legal action against such a private person for slander/defamation, you would have to prove on behalf of your mother that a 'false' statement was made about her, that it was intentionally made knowing it was false, that it was about a serious issue such as allegation of criminal or immoral conduct, and that it caused foreseeable financial and other damage. 'False' is not the same as a statement of opinion, 'catty gossip', nasty, mean spirited, impolite, etc. Without demonstrable damage, there is no case. It's not clear from your post what the rent discount issue is. And, truth is a defense to any slander claim.

If you have such proof and recoverable damages, the next practical question is whether you could ever expect to recover any money from the defendant if you did win a judgment. Without that, you'd be spending money' on principle' to pursue this.

If your question is about taking action against the complex and mgmt, then you need to provide more detail of what it is they did 'wrong' as a result of the gossip. They are bound by laws and the rules of the complex, regarding rent, costs, discipline, penalties, etc. If you think they violated those rules, then you'll have to explain how, and what damage it caused. A serious violation might justify a cause of action against them.

If you think you have a valid claim[s], with merit and collectability, feel free to contact me to discuss your options. Also, consider the potential of having a lawyer write a letter to the complex and/or the gossip person, demanding remedy of the problem, on threat of litigation.