"Can an employer be ordered to provide evidence of their claims?" Sure - by a court of law. An employer does not have to comply with an employee's request they provide proof of misconduct or poor job performance.
"The person in question feels that the employer was waiting for any mistake or complaint to come up that would allow them to fire her. Is this a difficult area to litigate in?" Yes, inasmuch as that is not unlawful.
"What are some possible responses to an action such as firing where the motives of the employer are purely malicious and may damage the reputation of the one they are firing?" Generally, none. If this was an "at will" employee, then an employer may terminate an employee for any reason except a specifically prohibited one. If the boss fired someone just to be mean, that makes him a jerk but it doesn't mean he violated any laws.
"The question now should be, what would YOU do if you felt that you were fired unfairly and that the firing might damage your ability to seek future employment?" Many people are fired for reasons they believe are unfair. (On the other hand and for example, I've fired people who were caught stealing redhanded and who thought it was unfair.) Nothing that has been shared in either post suggests there is any basis to pursue legal action. What the terminated individual needs to do is to pursue new employment opportunities and determine how to position the circumstances under which she left in the best possible light, while still being truthful. Lining up references who can attest to the quality of her work and character will be very helpful too.
