A Wubi install makes use of loopback mounts. Essentially it mounts your Windows file system, and then treats a file within that file system (your root file) as a block device. This basically means that rather than reading the blocks of the file system from a partition directly, it looks at the layout of the file in the other file system to locate each individual block. It isn't running the system out of RAM.
It then performs some gymnastics to make the loopback mounted file system appear as the root, and your Windows file system appear somewhere below the root.
As a general rule, you should not modify the backing file for a loopback mount, since it can confuse the file system driver that is referring to that file. It would seem the actions you took were not enough to cause these problems though.
On UNIX systems, once you open a file for access it is still possible to read it without causing problems. Consider the following short Python example:
with open('oldname', 'w') as fp:
with open('oldname', 'r') as fp:
As with your loopback mounted file system, we can still read the content after moving the file. We can see a similar effect when removing a file:
with open('newname', 'r') as fp:
While the file name is removed, the actual content sticks around until the last open file descriptor is closed. The loopback mount can be thought of as a file descriptor for these purposes.
Copying the file is also unlikely to confuse the loopback mount (since it is just reading the original), but is not necessarily a good way to perform a backup. It takes a while to read through a large file, so by the time you've got to the end of the file the start might have been modified. So if you try to use the copied file as a disk image, it may appear to be corrupted (although that corruption may be fixable with a file system check).
If you want to back up your system, I would suggest either using the backup tool included with Ubuntu, or booting to Windows and copying the disk image there (since Ubuntu is not running, there is no chance of the disk image changing while you're copying it).