Closing Tickets
Tickets can be closed or solved in Zendesk, and no replies or updates will be sent into Slack. Once a ticket is 'Closed' in Zendesk, it cannot be reopened. This means a follow-up ticket will be automatically created if another Slack reply is recieved.
Manually creating follow-up tickets in Zendesk is not supported, and will have no effect. Reply to the existing Slack thread to create a follow-up ticket.
Solved Tickets​
Solving a ticket in Zendesk is different than closing. When a ticket is solved, new replies from Slack will move the ticket back to an 'Open' state. A typical flow in Zendesk is to start by solving tickets, then use an automation to close solved tickets after a few days.
Deleting Slack Messages​
If a parent Slack message is deleted, it's corresponding Zendesk ticket is closed. This way, the ticket cannot be replied to from Zendesk since there's no thread to route to in Slack. See the guide on Deleting Slack Messages for more info on this case and more examples.