This article provides information on how auto-close rules affect satisfaction surveys from being sent out.
Sending the satisfaction survey is linked to ticket statuses. From the Admin Panel > Tickets > Statuses, you have the option to configure which status would trigger the survey - typically tied to the "closed" status.
This means that if Yes is selected on the 'Send satisfaction survey email' option (see screenshot above) and the ticket is changed to this status (i.e., closed), an email will be sent to the user asking for their rating and feedback.
The auto-close rule feature on the other hand is a feature that automatically changes the ticket status if it has been inactive for a certain length of time. So let's say you configured an auto-close rule that will change the ticket status to "closed" when there's no response from the customer within 72 hours, then a survey will be sent out once the ticket status has been changed to "closed" - granted that the 'Send satisfaction survey email' is enabled to the "closed" status.
When you set up an auto-close rule, you have the option to 'Suppress customer survey email', which when enabled, prevents the helpdesk from sending a survey invitation for automatically closed tickets.
To learn more about auto-close rules, visit the Resolving Tickets Automatically Using Auto-Close Rules article.