Nothing will happen to your clothes other than your clothes will be softened from the fabric softener but the fabric softener will not get the dirt or grime out of your clothing.
So if you wash your clothes with fabric softener you'll just have soft unclean clothing.
If you want your clothes clean you'll have to wash your clothes with laundry detergent along with the Fabric Softener if you want soft clean clothes.
You washing machine will not be harmed either so it doesn't matter you just won't have clean clothing.