Can a dissolved corporation's shares still be transferred to someone else?

Not in any meaningful practical sense while the corporation remains dissolved. Shares represent an ownership interest in a corporation, and once that corporation has been dissolved, there's no longer a functioning corporate entity with a share registry, directors, or officers able to record and give legal effect to a transfer. Someone can informally agree to sell or assign their interest, but the corporation itself can't actually process or recognize that transfer while it doesn't legally exist.

If the shares still have real value, whether because the corporation holds property, has a pending claim, or the parties simply want to formalize a change in ownership, reviving the corporation under the Business Corporations Act is generally the necessary first step. Revival restores the corporation's legal existence, which in turn restores the ability to properly update its share registry and give effect to a transfer through the corporation's own records.

Anyone trying to buy, sell, or transfer shares of a corporation that turns out to have been dissolved should treat that discovery as a reason to look into revival before proceeding, rather than trying to complete the transfer informally and sort out the corporate side later.