They are most likely encrypted with your public key, no?

Presumably your data is duplicated to the point that all nodes containing any particular piece of data are very unlikely to be offline at a given time.

I haven't had a chance to dig into this paper yet, but for a similar system Swarm [0], there is a system of insurance and escrow on file chunks, and a system of verifying the hash of piece of the file to see if they still have its contents.

[0] http://swarm-gateways.net/bzz:/theswarm.eth/

The file is encrypted locally before uploading to the network. Then the file is sharded, and the shards are replicated among the nodes. Once a shard falls below a certain replication threshold, it will get copied to a new node.

There are other schemes that don't require a copy of each shard, allowing you to reconstruct the file if any subset of the nodes is online.

I don't know how Filecoin strengthens reliability, but Sia splits your file to 30 small pieces and distributes them randomly among hosts. You only need 10 of the pieces to recover a file. So, in effect, you rely on 10 out of 30 random hosts to be online at the time of recovery. The chance of more than 20 random hosts that are holding your file are offline at the same time is extremely small as long as there's enough diversity among hosters (particularly many different hosting companies and many individual hosters in different regions, so hosting isn't mostly "centralized" to one region or company).

I think Sia's method would prove to be extremely reliable, but again, it depends on the hosters. If the largest single hoster owns less than a third of the capacity of the network, even if they suddenly go offline, you should be able to recover your file since you rely only on a third of the 30 hosts who hold your file to be online.

Also, I think that the number of pieces you need to recover a file can be tuned, so if 33% would prove to not be reliable enough, Sia/Filecoin can tune it down to increase reliability.