You're answering a question that no one is interested in. The problem isn't "can any singular instance of an encrypted output be compressed". That's a trivial conclusion -- as it's theoretically completely random bits, of course some combinations of those bits are going to be compressible, maybe even highly compressible. It might be that the encrypted output is entirely a single repeated byte, in which case a 4-gigabyte message could be compressed to 4 bytes (being the integer representing how many times to repeat the byte).

The real question is, can you reliably compress encrypted messages in general? And, given that the encryption is not broken, the answer is no.

In practice, with any real, widely used compression algorithm, encrypted output will never be compressed. You can generate 100,000 random binary files and run them through all the major compression tools and not one of them will compress by even a single bit.

In theory, some random outputs will be compressible by common tools (for example, a file that's all zeroes). However, the probability of encountering a random file that compresses more than the overhead from any common compression tool is vanishingly small.

> People are literally saying that a encrypted output can NEVER be compressed.

No they're not. They're saying that as a class, you cannot compress the data. That is a statement about what happens in aggregate. And the aggregate result of trying to compress securely-encrypted data is that you don't save bytes. Even just having the option of compression does not save bytes, because you have to store the choice.

Monkeys hitting random keys on a typewriter can write novels (although not all the time!)

Any one given input can be losslessly compressed down to 1 bit with the exact right compression algorithm. I think everyone here understands that. The argument is just that that's not really useful in the real world.

But, (also by the same ideas), most encrypted texts will not be able to be compressed by more than a single bit.