"Hit It Twice" Customer Service
jakeworth.com
jakeworth.com
If they accept the request for a call/chat, it's because they have more to say (good, bad, or otherwise), the first post-resolution response slipped past them (especially if the "first hit" goes out within a day of resolution, because they're probably catching up on time lost from the issue), or they're a rotating team and the main contact is out for a moment.
Closing the ticket in most of those circumstances would be premature from the customer's perspective, whether they report that negative sentiment back to you or not. There might be another issue exposed by the resolution of the first issue that wasn't evident, or they might have feedback or want a bug tracker ticket to follow if the issue was a problem with the product or docs.
On the other hand, if they see the request for a call and their issue is fully solved, they'll appreciate the offer for synchronous time even (often especially) if they refuse it. It signals an openness to communicate both ways that isn't limited to "I have a problem" and "Fill out this NPS survey".
And many customer contacts hate unnecessary calls/chats enough to consider this a warning that you might push harder for one before closing the ticket, so they'll just close the ticket themselves to actively avoid the "threat" of the call.
The notification that the ticket is being closed should come 2-3 business days after that last offer for a call/chat. If they want to talk to you again, it's in another ticket.
If a lack of agent capacity prevents offering synchronous wrap-up calls/chats before closure, reserve them for escalated tickets and offer them as the manager. If it turns into a support call, open a new ticket and hand them back off. If not, you're in the perfect position to get first-hand customer feedback about a fresh support interaction.