Diana, are you confusing the molted skin of the nymphal cicada? That's what we all find attached to fence posts, tree trunks, or anything those little things can grab on to as they make their way out of the soil. The adults don't molt. Any winged insect has completed all of the molting it is ever going to do. As a matter of fact, the cicada completes all of its molts but ONE under the soil. When it crawls out of that nymphal skin, it emerges as a winged adult. I suspect the 'freeze mode' was because this insect was nearly dead. Remember, they spend 3 to 17 years (depending upon the species) in the soil, but only a few days as flying adults. Here is a link that might be useful:

It could be a cockroach, one of the inoffensive species. Or it could be a leaf. Maybe a closer shot? No excuse for a bad photo of something that isn't running away! :P Location helps too.

Other than the arborvitaes (and their leafminer IS a moth). Most leafiners are more of a cosmetic issue than something that actually harms plants. I never bother to treat for them. And beneficial wasps parasitize a lot more problem pests than just leafminer larvae. I would encourage them before I'd try to eliminate something else that is really not much of a problem at all.

Second image, not parasitism, but rather leaf beetle larvae and their fecal shields.