Is there something as self-completing data transfer, like Sudoku?
What you are suggesting is indeed rooted on concepts that are important in DSP: 


On the channel coding side, you have for instance error correction codes (or error correcting codes, both ECC)
On the source coding side, since you mention Sudoku, techniques like matrix completion, sparse sampling or compressive sensing are possibilities to approximately recover incomplete grids.


However, they work on assumptions on data like positivity, sparsity), and approximate recovery. I have not seen yet such a scheme working for universal lossless compression. An argument is derived from the Dirichlet or pigeonhole principle, another one is easier with recursion. Suppose you have a clever scheme that self-completes data packages, based on some functions that combine inputs. For compression, you expect that it turns all  $B$ bit-stored file on a smaller number of bits, say $B-1$ bits or ledd. Then you could apply it again, and again, until you reach $0$ bits, which does not make sense.

So, this does not appear possible, unless you have additional assumptions that could reduce the space of possible data.