Years ago OSM had some distributed solutions, like OSM@home (dead before 2007) and Tiles@home (dead before 2012). It is prehistoric for such a dynamic project as OpenStreetMap and basically nothing else happened since then (Mapeo might be one of the specific exceptions). Currently however new generic P2P mapping project emerges - Peermaps:
It is based on the next generation web frameworks, called Dat and IPFS (InterPlanetary File System), so it does not have to deal with all the basic stuff, since this is already done as universal groundwork solutions (not limited to maps or any other kind of distributed data) and growing in usage:
https://en.wikipedia.org/wiki/Dat_(software)
https://en.wikipedia.org/wiki/InterPlanetary_File_System
The project is in the infancy, so just look at some random up-to-date details:
- https://github.com/peermaps/roadmap
- https://github.com/ipfs/devgrants/pull/41
- https://github.com/peermaps/docs/blob/master/bufferschema.md
- UI mockups: