Open processes will hold open their files. So long as it's an 'rm' that you've run (which merely removes directory entries) and not a destructive action on the disk contents themselves, it's often possible for things to continue in a startlingly unaffected manner. Though not always.
The extent to which new calls to deleted files are made will have a strong impact on this.
The extent to which new calls to deleted files are made will have a strong impact on this.