If its owner deletes the data, and no other copies exist, and no one uploads identical data using the same owner keys, it’ll eventually get garbage collected subject to free space pressure.
The handy part of this is if you delete everything from SAFE, and then reupload it again, the network will spot that the chunks are already uploaded and you don’t actually need to upload anything.
If you’re more worried about the privacy/security thing that deleting data doesn’t really delete data, that’s already the case for any filing system, and any cloud storage. Nobody actually deletes data, they simply flag the data as deleted and they may or may not garbage collect some day.
The big difference with SAFE is that the connection between data and its owner is one way. There is no mathematically feasible way of figuring out who owns some chunk. If one were the NSA and could watch the entire internet, one could watch network traffic patterns in SAFE to infer connections between chunks and owners, but even then you can only narrow an owner down to their local group at best, so that’s a 1 out of 32 chance, and this is assuming the attacker has a 100% opacity on all global internet traffic flows.
And let me turn it the other way round. If you have some data which you need to delete in a hurry because someone is coming for you in the next five minutes, the very last thing SAFE should do is actually delete anything because that identifies the chunks belonging to you. Far better simply to disconnect you mathematically from your data using an entirely local operation of destroying your encryption keys.
Niall