Primitive runs like 0000000 are compressible patterns. Other patterns similarly, like 01010101, or 00110001110011. That's why you check generators visually by printing out bitmaps, and ideally by running it through a couple of compressors. Afaik this is not yet done by the 4 most common PRNG testsuites yet, but I'm working on it.

When you compress 0000000 to something smaller, you have to replace '0000000' in the plaintext with a smaller symbol in the squash text. Which means if that smaller symbol appears in the plaintext, you have to replace it with a larger symbol in the squash text. And if your smaller symbol appears more frequently than '0000000', you are going to end up with a "squash" text that is larger than the plaintext.

True hardware random generators regularly have runs or non-uniformity. That’s why we use them to seed a CSPRNG not use the output directly.

Example https://crypto.stackexchange.com/questions/38053/what-should...