Legal Question in Business Law in California

You question is too vague and general to answer. You can sue anyone for anything, but presumably you are asking if there would be a meritorious case. That can't be answered based on vague generalities.

I'll assume you mean "Can an assisted living facility be sued successfully if...."

The answer is that the employer would probably, in many cases, be liable to employee #1 for harm done to #1 by a forgery committed by employee #2 if the employer were also negligent to some significant extent, and the negligence was a contributory factor in causing the harm. For example, the employer might have negligently failed to discover that #2 had recently been discharged from prison after serving 5 years for fraud, or the care facility may have failed to install and use audit procedures that could have made the forgery impossible.

There is also the theory of "respondeat superior" (legal Latin for "Let the master answer") in which the master (employer) is held liable for certain misdeeds of its employees. There are several good discussions of "respondeat superior" available from a Google search for that term, including Wikipedia. A requirement for this theory to apply is that the misdeed must have been committed in the course and scope of the employment.

If neither "respondeat superior" applies nor you can prove some contributory negligence on the employer's part, a successful suit is probably unlikely.