Note that Briar's darknet nature makes it not have a shared/social store-and-forward system.
However, it does exchange messages with contacts whenever possible, recently added a file-based message transfer method (think dead-drop USB/microSD), and gossips message DAGs in forums and group chats (forums lack a leader; groups chat leaders can kick a member out but have to personally invite every member).
https://briarproject.org/how-it-works/
https://news.ycombinator.com/item?id=29227754