Breaking a gene during recombination
Yes, you could imagine a situation where two functional alleles could produce a recombinant which was non-functional.

chromosome 1 has A and B at positions x and y - functional
chromosome 2 has C and D at positions x and y - functional
Recombination between positions x and y produces A/D and C/B versions of the gene. Either or both of these could be non-functional.

Nothing prevents this from happening, but natural selection will act on the recombinants.