How to avoid that that a user has two opened issues in Jira?
Technically, you can do that with Behaviours plugin.
It needs a Groovy script that looks up the reporter's other issues and transitions them to a paused.
Hovewer, I don't advise doing this, because you'll also need a carefully crafted workflow that supports your "Pause" transition on all statuses, a working Groovy script (needs programming experience, and intense knowledge how JIRA API works). Also needs another script that reopens the previous issue when the newest one is closed, etcetc, there are a lot of pitfalls.
How to avoid that that a user has two opened issues in Jira?
It's possible that Jira treat issue management in this way:
when a user has a issue opened and will open another issue, this first one must be automatically paused?