In this paper on pg. 1248 in the "preprocessing phase" section the authors say:
In the preprocessing phase, the parties run a (standard) MPC to collectively generate a key pair (pk,sk) for the FHE scheme, and to secret share sk in such a way that (a) learning the shares of corrupted parties, and leakage on each remaining share, does not damage the security of the FHE, but (b) collectively, the shares can be used to evaluate the decryption circuit in a leaky environment
Part (a) above makes me believe there is a risk with FHE security being damaged. Is it possible to use another encryption scheme where this risk is mitigated ?