Thanks for the question, here are some thoughts on this topic

Since each secret share of a FROST key is a point (index, secret share) that belongs to a polynomial with some interpolation threshold. A threshold number of parties can each evaluate their share of this joint polynomial at a new participant index.

Parties securely communicate these evaluations to the new party using a repairable threshold scheme, and the new party sums them to receive their secret share. This secret share belongs to the same polynomial and key as the other parties, can sign etc.

Removing a signer involves parties recreating their secret shares and a new polynomial, only this new polynomial retains the same joint-secret (x=0) and thus the same public key.

The removed signer never loses their secret share, only they will now be incompatible with every honest signer who has moved to a new polynomial.