No they can't. If you elect to retain your shares, there's nothing they can do about it.
Whether you want to or not is a decision for yourself only, unless there's a takeover/scheme of arrangement, in which case you still get to vote on it, but are bound by the outcome of that vote.
Participating in a buyback can be a great opportunity though, as it allows you to cement a capital loss which can be use to offset taxation on future capital gains.
Definitely worth thinking about carefully.
I still hold a stock that I bought into 15 years ago and have since declined to participate in multiple unmarketable parcel buybacks, purely because it wasn't a large investment and it's a constant reminder of mistakes I've made in the past and lessons learned from them.
At close of trade today, that holding is currently worth the handsome sum of $13.90. LOL
