The usual advice I've seen on the forum is to unwrap and set on cooling racks before thawing. But humidity is often high here in Michigan, and cold cupcakes collect condensation. And sadly, wet frosting/fondant/gumpaste tends to dissolve. So I'd like to defrost my iced and decorated cupcakes fully before ever opening the plastic container I froze them in.

Does this always result in the liners coming loose? Maybe it's cheap paper liners that do, or do waxed or foil liners loosen also?

With all chocolates, petit fours, fondant cakes, fondant cookies, etc. I TRIPLE wrap them when I freeze. I defrost by cooling at room temp for 8 hours IN THE WRAPPINGS. The condensation won't form, no more shiny, wet baked goods. I don't know about your liner problem, though - it never happened to me.