I have heard it anecdotically that non-bijective sboxes are potentially weaker to be used in designs like feistel networks. (since by design, it is allowed for the sbox to be non-reversible)
Is that a fact?
The first thought I had on this was that it may related to the fact that the probabilities of S are not uniformly distributed and so, if you choose the most favorable outcomes you may have an edge over the bijective counterpart in e.g. bruteforcing.
But again I new to the field, so any insights on the matter would be greatly appreciated.