Well, all right, I could use conventional compression such that S2 is zero, by making S1 what would have been S1 + S2. That still leaves the "compressed image" having zero bytes, by hiding the actual compressed image in the executable.

Note well: I am not claiming that there is any reasonable reason to do this. It's just a way to say "well acksually..."

Notice how you had to change the wording in this comment to make the scenario work. If the problem statement is "compressing 1GB to zero bytes" or "decompress 1GB from zero bytes" then that trick is easily called out as invalid.

So your way around is by baking the data into the executable instead?

How good of a ”solution” is that in reality? Like what if you were tasked to decompress multiple different files? Would you bake does into the executable aswell?

Personally, I would count this way around as invalid.