They will rust out. I have caught bass with rusty hooks sticking out of their butts. Really, no kidding. The swallowed hook often passes. The stomach acid corrodes the hook and takes the edge and temper out of the steel. I have also caught fish with rusty remnants of hooks and lures sticking out of their jaws.
when I gut hook a fish, I can sometimees reach through the gills and take wire cutters and cut off the barb. After I do that, the rest of the hook slips out easily. Or, I pull the hook, pushing the barb in the direction the hook is pointing. I then cut the line after the hook is free. That way I do not have to fight the barb. Do not try to free a barb that is sticking in a bass by "fighting" the barb.
If a hook is sticking in "your" lip, do you think it would be better to push the point out of the flesh it is in, freeing the barb, or force the barb out by pulling in the direction opposite where the point is sticking ?
If you can't get the hook out, release fish with hook imbedded.