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Tickets are automatically removed from the board after 14 days and for that, the tickets must be on the very last column that is where the resolution is set.
Cards in the last column of your board are always categorized as done, meaning all work has been completed and the task has been carried out. If you’ve enabled the sprints feature, these issues won’t return to the backlog when you complete your sprint. If you don’t have the sprints feature enabled, these issues are automatically removed from the board after 14 days.
There is a feature request suggesting the implementation of this ability:
Please, click on vote and watch to receive updates about the feature.
As far as I'm aware, Next Gen boards have something set that tasks will disappear from the right hand column after they've been in that column for a certain time (10 days? 14 days?) The ability to configure that time period isn't available yet, but will be at some point in the future.
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