The contents become inaccessible to everyone via that name. However, the original contents are still in the original writer's store and any previous snapshots will point to it so it is still available (assuming a snapshot happened twixt the two writes).
Upspin is at heart a write once storage system. When you overwrite something, nothing goes away. You are adding blocks with the new contents to the store, and rewriting the directory tree (also just blocks in the store) up to the root. Our snapshots are just a list of directory entries pointing to the roots at the time they were made. Thus (1) snapshots are fast and take very little room and (2) represent the directory tree and contents exactly as it was at the time of the snapshot.
The flip side is garbage collection. We don't have infinite storage. We have a few attempts at garbage collectors though nothing to write home about, actually something the community could help with. To clean up blocks that no longer are referenced, one has to descend down the current tree and all snapshots marking blocks as one goes. Any not referenced can be removed. Ditto one could conceivably trim the number of snapshots to reduce the referenced blocks.
The fly in the garbage collection ointment is actually related to your question. If you write into someone else's directory tree, the blocks are in your store. They will not be referenced in your directory tree or snapshots. Therefore, garbage collection will not know about them. I do not have a good solution to that since you won't necessarily be able to walk their tree even if you know it is there. One could indeed occasionally copy foreign blocks into ones own store that would be a possible solution.