It is not possible to compress arbitrary data. If the data is already compressed, or it is encrypted, or it is randomly generated, it cannot be compressed with any method. This is foundational information theory.
Whereas if we're talking about lossy compression (as is the person to whom you replied) we certainly can compress arbitrary data - almost as much as we want.
The hard question, then, is how much the decompressed output looks like the original.
The hard question, then, is how much the decompressed output looks like the original.