When you delete an agent from Freshdesk, all tickets assigned to that agent will automatically become unassigned and the agent would be converted into a customer in your Freshdesk Account.
A deleted agent is not permanently removed from your Freshdesk account. This is because all data in Freshdesk, including tags, tickets, and activities are associated with the agents in Freshdesk. The agent would be available as a contact in the customers' tab of the portal.
Pro Tip - Before deleting the agent - assume their identity. Please navigate to the Tickets page and filter all tickets (open, closed, pending, resolved, etc) that are assigned to that agent and do a Bulk Action to re-assign them to another agent. Then, you could delete the agent without having to worry about which unassigned tickets were originally assigned to them.
Alternatively, you could also change the agent's type to the occasional agent by going to Admin > Team > Agents > Edit agent by selecting the particular agent. This way, you will free up an agent seat and you can retain the record of tickets assigned to the agent. If you also want to make sure that the agent won't be able to log in again, you can change the email address of the agent.