BEEFY must deal with equivocations. That includes at least:

• detect equivocations
• report equivocations
• initiate slashing

Also, since BEEFY is based on GRANDPA, there is an edge case that Alistair mentioned:

We can have BEEFY validators slashable for voting for something on a different fork when this one was finalised. This is not quite an equivocation, and we should cancel the slash if they can point out a valid GRANDPA justification for the fork they voted for.