They give up and switch to Windows (again).

The highest profile was in Munich where they did migrate >10,000 desktops to Linux and OpenOffice, but eventually they migrated back to Windows and Office:

https://en.wikipedia.org/wiki/LiMux

Lower Saxony:

https://www.zdnet.com/article/windows-scores-a-win-over-linu...

Vienna:

https://en.wikipedia.org/wiki/Wienux

Note that even when these projects succeed, the software users are running is invariably just Firefox, and often users have both a Windows and Linux PC side by side. There are no actual Linux apps being developed or maintained, in the sense of apps that use Linux APIs.