Can triggers or automations set off by the event of a ticket being unshared with another Support account?
No, there is not currently a condition within business rules that accounts for the event of unsharing a ticket.
A workaround to this would be to utilize macros that apply a tag when an agent unshares a ticket. In this workaround, the agent would apply a macro adding that tag when they unshare a ticket. From there, a trigger or automation could be created to run whenever a ticket is updated with your unsharing tag. For information on macros, see Using macros to update tickets.