Lettie, If by "save files" you mean save the state the guest XP and all its open files are in when the host shuts down, the answer is Maybe. The Virtualbox manual, section 9.26, discusses what the guest may do if you suspend (Windows Hibernate) the host. Essentially, when your Windows or Mac host hibernates the guests all pause. Waking up restores the running guest. Linux hosts don't have this yet.
Getting the guest to happily save itself when the host shuts down, logs off, or reboots is not handled by Virtualbox. In Windows there are Group Policy settings to run a script when the OS shuts down, but these scripts run long after a guest will be mercilessly killed by the shutting-down host OS. You have to keep your computer from shutting down, logging off, or rebooting while you are running guests.
If it is really important to keep that guest from dying unceremoniously, google for how to remove Shut Down, Log Off and Restart from your Start Button power choices. Use shutdown and restart scripts that check for and save-state the guests before shutting down, logging off, or rebooting the host. Get the battery backup to hibernate instead of shut down. Use a
scheduled script to handle Windows Updates instead of letting the OS handle updates itself, and insert guest-save-state commands before the host shutdown command.
Another possibility if your host is Windows is to run your guest as a service: See
viewtopic.php?f=6&t=8595&start=30. The guest will run when the computer boots before you log in, then you remote into the guest using Remote Desktop to see the guest via built-in Remote Desktop, Virtualbox's Remote Desktop, or in-the-guest remote-in software. The guest can be set to save-state before the host shuts down.