We have a family member who doesn't have citizenship of a Schengen country. She lives in South America and has no intention in moving to the EU other then regular visits. This is now done on Schengen multiple entry visa. The 90/180 rule and the bureaucracy when the visa needs to be renewed can be time consuming an annoying. Because of a funeral of her father was missed. Currently we have to postpone an invitation because a renewal of her passport required a new Schengen visa, with al the bureaucracy needed.
Since her family all resides in Schengen member states we are wondering if there is some sort of resident permit, which would allow staying in Schengen while at the same time residing in a non-Schengen country.