I store everything in Calibre. When I buy an eBook from Amazon, the first thing I do is strip the DRM. Because even though I'm basically happy with my Kindle library, I don't want to lose all my stuff if they change their policies to something I'm not happy with in the future.
So I'm doing most of my library management from a PC, but doing most of my reading from a Kindle Fire. There's no great solution for this, so I've just been taking the books that I'm actively reading and copying them into Dropbox.
This is an interesting project, and I'm sure I'll try it out. But I'm skeptical of using a browser-based book reader on my Kindle. Say what you want about Amazon, their native reading app is still the best I've ever seen by far. Meanwhile, even Amazon's own web-based reader is crap.
It's also synced automatically to an external hard drive connected to the Raspberry Pi, so I have two backups (one online, one offline) in case something goes wrong.
I haven't tried using a source control system, that might work better. Hmmm.
And of course that only works for computers, There isn't a full version of Calibre for Android.
I'm asking because I use Dropbox to store my Keepass DB, and so far (2+ years) I haven't had any problems.
I do the Keepass thing too, and this has happened with it's files as well, but that doesn't seem to cause any problems.
To the layman, any situation that results in having Calibre show books which are not in fact there, or having books in the library which are not shown in Calibre, or having Calibre's check library function report that there are "invalid titles", "missing formats" etc., could be casually described as "corruption".