You can reopen both a resolved and a closed issue in JIRA. What's the practical difference? (besides requiring different permissions to resolve/close issues e.g. if QA is involved)
We have some differences of opinion in our team for whether to resolve or close, and I'd like to point towards some authority and say "we should do it this way".
Typical issue workflow is the person working on the bug resolves it, and the person who opened the bug is the one who decides if the resolution is acceptable. If it is, they close it. If not, they re-open the bug for further discussion/work/wrangling.
The exception to this is when a bug is a duplicate, often the person who is working on the bug realizes that it's a duplicate, and can then close the bug themselves as a duplicate. Or maybe they resolve it as a duplicate, the opener agrees, and closes it.
IIRC, JIRA has a pretty flexible (if complicated) workflow, so you can setup any process you feel is appropriate for your team and the groups who will be submitting issues.
Edit: I realize I didn't actually address reopening closed issues. In my experience, it often doesn't happen because people search the issue system for existing bugs that exhibit the same behavior as what they are seeing. And that's if you are lucky, quite often bugs get opened without any investigation into existing issues.
That being said, a QA or field person will go "I remember that bug. Dammit, they said it was fixed" some time after the original owner closed it. At this point, they may reopen the old bug, or create a new one and link to the original. My preference is for there to be a new bug and to link, rather than reopen. The reason is that the "new" issue may exhibit the same behavior, but might have a completely different cause. This is often the case when really generic error log messages get spit out.