In a survival situation, such as fleeing to the mountains, or simply being lost in the woods, is it permissible to consume unclean animals: grubs, insects, etc.?

Those questions are argued among the members.

Some will say, no, scripture says don't eat those things, so trust in the Lord to provide something you can eat, don't eat the abominable things. Don't compromise. Jesus could have turned stones into bread and ate, when He was starving, but didn't.

Other's will say, "but the health message is about eating the best foods available in order to possess health. If that's the best food available and you are starving, starving is not healthy, eat what's there.
What's wrong with a good rabbit stew cooked with edible plants?

probably a better response is to get familiar with the plants and other items out there that are edible which don't compromise God's law.

According to the Bible you can eat grasshoppers and locusts, certain fowl, and fish, as well as plants and berries. There's a whole lot more edible things out there, than people generally realize.
Your question kind of alerts us, we should be more familiar with some kosher eating in the wild.

But as to a definitive answer to your question, basically, no person can answer for another who finds themselves in a really serious state.
It's between the person and God.

Elijah was fed by the ravens.

"He will dwell on high; His place of defense will be the fortress of rocks; Bread will be given him, His water will be sure." Isa 33:16

Yes, Elijah was fed by the ravens, which is different Elijah than eating the ravens.

I've read more than one story where someone in a survival situation thought they needed to eat unclean animals. They got sick and said never again.

I would have a hard time coming up with a natural situation where there were only unclean animals available and not clean. In fact, I would have a hard time imagining a situation where one would need to eat animals. Just eat the plants the animals are eating. And if the animals are starving because of no plants, would you go against health instruction just to live a couple more days?

However, in an unnatural soylent green type of situation where the only food might be packaged grubs, ants, and cockroaches (or other things!) distributed, one would need to question if it was possible to flee to the remote areas and why not do so.

Well, just for example, if you studied deeper on most places even remote areas, there are hundreds of plants, shrubs and fruit off trees, etc.. before you would have to eat a snake or a rat.