Any tickets assigned to an agent who is removed will become unassigned.
Deleting users from your account soft deletes them, and that means that the users are still in the Zendesk database and accessible on a limited basis only to Zendesk employees with certain database privileges.
You can't delete an end user or agent who's a requester on a ticket that hasn't been closed yet. See Solved vs. Closed tickets. First, the ticket must be solved before it can be closed. Second, the solved ticket must be closed by a trigger or an automation. The ticket can't be closed directly in the agent interface.
For more details about deleting a user, see Deleting a user.