Ask HN: Is there an open source license that requires you share data collected?
So, let's say you open source a web chat program. Is it possible to specify it is free to use but you must share any data collected with the research community.
If not, would such a license be feasible legally?
as far as your actual question - it depends on what "data collected" you're referring to. Can any of the data identify the users, etc? If you provide an API that they need to plug into, or make it all SAAS then sure, it's at least physically feasible at this point.
But it almost sounds to me like you're asking people to manually send them data from some local installation - or you want to send them a demand notice for system data if they don't - or you want to prevent them from blocking some monitoring service. To me that does not sound realistic even if it was legally feasible.