What happens when your employer loses your review and is not willing to pay full back pay from when it was done?

It depends on what you mean by pay full back pay. That is,

1) If you worked, you *must* be paid for the hours worked at the hourly rate then in effect for you (or if salaried, you have to receive you salary for weeks worked; or if a commissioned employee with a commission plan, they have to commission you at the then-in-force rate; etc.). So being paid your wage/salary/etc. should not depend on your review.

1a) Even if your review was awful, they'd still have to pay you for work done--though they could always fire you going forward.

2) If by "review" you mean a time record, then under the law the employer still needs to pay you for all the work you did, and the issue becomes can you show the work or hours that you performed. Sloppy record keeping often puts a company at a disadvantage in these cases--the law favors paying employees--so if this is the case and you have any evidence on your side, you should be in a good position.

3) If the issue is that they may have given you a discretionary bonus or pay of some kind if your review was good enough, then you might not have recourse, since if it was discretionary (rather than based on a formula, on hours worked, etc.), the company could choose to not pay it for any reason.