Ming Lai wants to know how backup programs handle files that are currently open and changing.
Ming actually asked something much more specific: How does Mozy backup open TrueCrypt vault files. I'll give you a more general answer, applicable to anyone who uses backup software, followed by some specifics about those two programs (both of which I use regularly).
Most good, current backup programs, including Mozy, use Windows Volume Shadow Service (VSS). Introduced with Windows XP, VSS takes a snapshot of open files, creating what are basically temporary read-only copies that can be backed up by any VSS-capable program. It's a nifty way around Windows' habit of not letting you mess with an open file.
This is a nice convenience--you can backup while you work, something that really wasn't practical before VSS. But it has its downside: Changes you make to the file in the course of the backup won't get safely copied until the next backup.
For instance, Mozy is backing up my system as I write this (really). If this file becomes hopelessly corrupted tomorrow morning and I have to restore it from the backup, I won't get this paragraph back. (The next day: Fortunately, that didn't happen.)
TrueCrypt vault files have another issue: Since they contain other files, they can be quite large (I've got one that's over 200MB). And for security reasons, you really want to back up the vault rather than the files inside of it. If you're backing up online, a 200MB file can slow things down horribly.
To avoid this problem, Mozy seldom backs up large files in their entirety. Instead it usually backs up only the parts that have changed, basically creating patches that can be used to recreate various versions of the file. Of course, it can't keep patching the file forever. Every so often it decides it needs to back up the whole file. That's when I have to leave the PC running all night.