When using EncFS to encrypt a file on a VPS, will the file be stored encrypted or unencrypted in the automated back-ups taken by the host? (Assuming that the file is unlocked when the back-up is taken)
It depends on what the automatic backups are doing.
So, with EncFS, you will have something like
If the automated backup is doing, say, volume snapshots, so it's just looking at what you have physically have on the disk, it should only be picking up the ciphertext.
If the backup process is seeing what mounts you have, and running across those (trivially, something like
You will have to ask your service provider to see what they're doing, if they're picking up mounted filesystems other than what's physically present. If they are picking up all mounted filesystems (I think this would be unlikely), the plaintext may be getting backed up.
(I suppose you can also look at the backup/restore interface they provide you with, and see if you can restore plaintext)