Alaska is an At-Will state. That means the person can be fired for any or no reason at all, as long as the reason is not protected by law.
None of the protections listed were applicable to the victim of a crime that caused the company damages. Incurring damages through the actions of an employee, like mishandling a machine, crashing a company car or losing company property seems to be a valid reason to fire the employee.
So whether it is legal to keep the money from her paycheck, instead of paying them in full and demanding the money afterwards... I don't know. My best guess would be "no, not without sueing her first". But that probably isn't really the question here.
The company seems to be in their rights to fire them. Even without actual damages, "I think you are to gullible to do this job" is a reason with no protections by the law. Which is pretty much the ultimate punishment in employer/employee relationships.
Whether the person sees 300$ for continued employement as a deal worth taking, and an employer that blackmails their employees that way ("pay me or else") worth working for, is up to them.
Obviously, a specific contract could override anything above. Make sure you read the employment contract carefully if there is anything in there about such a situation or about mitigating at-will employment.