A ticket's final status is 'Closed.' To indicate the requester's agreement with the solution, industry best practise dictates that you let the requester close the ticket after the agent changes the status to 'Resolved.' If they believe the problem has not been resolved, they can simply respond to your ticket and remove it from the 'Resolved' pile.
When agents close a ticket, the email notification sent to customers is the best time to send out a satisfaction survey and learn how your customers feel about your support.
Most customers either forget to close the ticket or are unaware that they are required to do so. This means that resolved but unclosed tickets may accumulate in your helpdesk. To avoid this, consider creating a business rule that automatically closes all resolved tickets after a certain amount of time has passed (preferably after 48 hours).