This is probably more of a philosophical question. I've always kept issues assigned to the last person that actually closes the ticket. Recently, I have a user that is changing the Assignee from himself to Unassigned when he closes the ticket. Before I ask him to keep himself as the Assignee, I thought I'd ask the community for some advice.
Can anyone give me the pros and cons? Or, does it really matter since it is closed?
As a starting point, no. You should leave the assignee on the issue for the simple reason that it can be handy to be able to do things like "of all the closed issues, who last worked on them?" and if someone is removing themselves, you lose the ability to report that.
There is only one benefit of removing yourself as assignee - the "assigned to me" filter works. But that usually indicates the person doesn't understand what "closed" is, as the "assigned to me" filter is almost always coupled with "and still open".
It's very likely that your user is simply wasting their time and needs a little help grasping basic Jira reporting.
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