Going in the other direction as suggested in the comment, we notice that:
9056 / 2 = 4528
528 / 2 = 264
So the pattern could also be dividing by 2 and removing the leading digit.
Using this approach we get
Allowing for inefficiency in the descriptions of digits,
here are 12 digit sequences that describe themselves
and cannot be decomposed into smaller
Allowing for infinitely long periodically repeating sequences as well,
here are 8 trivial indecomposable periodically repeating infinite solutions
until more interesting ones crop up.
All of these ...