Files bigger than the number of bytes that a 32 bit integer can reference are usually called largefiles. Most modern UNIX-es have support for it with either oddly-named non-standard calls like fopen64() or some kind of more modern filesystem.

If you have LARGEFILE support and no disk quota enabled, you can essentially create a file that has size equal to the free space available on the disk. This is a BAD idea in general. sysadmins love to hate giant files, especially small files with giant holes in them....