Hello Kai,

Yes, it is possible to prevent duplicate subscription in Payplans you can achive this by these following method.

1.To prevent a user to subscribing from duplicate plan you can disable the option of Display Existing Subscribed Plans from the payplans backend you can find this setting here: backend>>Settings>>Plans>>Display Existing Subscribed Plans
Please see attached screenshot :screenshot
If you disable this option it will make plan disappear from your website for the user who already subscribed for it and if the user cannot see the plan they simply cannot subscribe it again.

2.One more way to achieve this is creating a limit subscription plan from the backend and setting the plan limit to 1 if you use this setting then user can only be able to subscribe the plan for one time and if they try to subscribe the plan again it will restrict the user to do so.
You can find this setting here: backend>>Plans>>Limit subscription
Pease see attatched screenshot:screenshot2
Read this documentation to learn more:https://stackideas.com/docs/payplans/administrators/plans/plan-limit-subscription

Have site with duplicate subscriptions, so it must be a bug somewhere since the users buy a new subscription, even they have a active subscription.

No, this is not a bug because multiple clients have multiple different workflow for their sites some clients also want their users to subscribe to duplicate plans based on there sites workflow.

Let me know if you have any other query.