The voltage drops, your computer switches off and, if you're unlucky, you kill your ups completely. Think of overloading the power grid (black or brown outs) or short circuiting a battery (ooooh, sparks and pop)
Well, I need to disagree. I am using a 600VA/360W Zebronics UPS from 2 years with my PSU being 600W. Had no problems with the UPS, but backup time is like for only 40-50 secs, I'd just off my system instantly if my power goes off. I also dont have any performance issues too..