If you're interested in this, it's a good idea reading about the Hutter prize (https://en.wikipedia.org/wiki/Hutter_Prize) and going from there.
In general, lossless compression works by predicting the next (letter/token/frame) and then encoding the difference from the prediction in the data stream succinctly. The better you predict, the less you need to encode, the better you compress.
The flip side of this is that all fields of compression have a lot to gain from progress in AI.
Fabrice Bellard's nncp (mentioned in a different comment) leads.
If you have a predictor/compressor LLM which was trained on all the movies in the world, would that not also be infringement?
An LLM is (or can be used) as a compression algorithm, but it is not compressed data. It is possible to have an overfit algorithm exactly predict (or reproduce) an output, but it’s not possible for one to reproduce all the outputs due to the pigeonhole principle.
To reiterate - LLMs are not compressed data.