How to fix pierced refrigerator liner?

If they use the old R-12 refrigerant then trash them. If they are newer and use R-134-A then maybe they are worth repairing. They make a viable epoxy patch material that is designed to be used on evaporators. You can purchase the kit at refrigeration supply houses. You will need a vacuum pump, refrigeration hose/gauge set, line taps, a torch, solder, flux paste,refrigerant scales and refrigerant (and a few other tools). If the investment in all these tools and supplies makes sense to you, the decision is yours. Otherwise, go a different route. I believe I would.