Well first off, through ~~God~~ Linux, all things are possible. You can have multiple hard links to a file, where a given hard link is deleted, but you can still manipulate the file through any other other links. Alternately, you can open a file, and while you have a valid open file descriptor, delete the file. The file descriptor is still valid until you close the file though, so you can still save (thus move) it to a new location.

Windows locks files when you open them, preventing these kinds of shenanigans.