Emacs gives you an error message in that case rather than destroying the old version of the file and then failing to completely write the new version, in the cases where it does the tempfile-then-rename dance. This is usually vastly preferable if Emacs or your computer crashes before you manage to free up enough space for a successful save.

It doesn't cease all operation; other Emacs features work as they normally do. Bash, by contrast, stops being able to tab-complete filenames, at precisely the time when you most need to be able to rapidly manipulate your files. At least, that's the case with the default completion setup in a few recent versions of Ubuntu.