Crypto-Compression Algorithms?
Unlike some crypto tasks like encryption+authentication combining compression+encryption have nothing in common/non synergies, so combining them into one algorithm offers no advantages.

In practice this means you first compress your data, and then encrypt it, because encrypted data is uncompressable. That way you cleanly separated the separate concerns, and you can vary them independently.

A good point to combine them is at the protocol/fileformat level. For example TLS supports compression and encryption, as do most archive formats(zip, rar, 7z,...).

But compression can hurt security: Typical encryption is designed to hide everything about the data, except its length. Compression depends on the data itself and affects the length of the data. That means that it can leak information about the data through the length bypassing the encryption. This is particularly severe if you compress data chosen by the attacker and secret data within the same context. This lead to the CRIME attack against TLS compression.