So, the Collings Foundation and their touring warbirds were in town recently, and we went to visit them. While out on the ramp though, my father managed to lose one of the Styrofoam coffee/drink cups the FBO provides (for their complimentary ice water and iced tea, of course). How much FOD hazard could that runaway Styrofoam cup pose, considering its relative lack of hardness and stiffness/strength compared to most other FOD hazard items?
Probably very little. There's the very slight chance that it could stuck on a pitot tube or some other terrible scenario in a Final Destination type film which, coupled with another issue, could cause a problem but again very unlikely.
The underlying hazard is the attitude towards FOD in general. It's a bad habit to build complacency towards any FOD sitting on a parking apron or letting it "get away". If it's SAFE to pickup the FOD then it should be picked up. It's possible the next time someone ignores a cup, it could have been used by a wayward mechanic to hold a sticky chemical that would ruin a pilot's windshield and his day if it smacks and smears on the glass on takeoff. Again very unlikely but why risk it!
If any engine fails due to a foam cup it was already failing. Obviously you never want fod on the flight line but there's a significant difference between soft and hard fod.
Chances of it causing a real damage are slim but not at all negligible. Shredded by a propeller may end up in a pitot probe and clog it. Best example of this sort of small thing big trouble is the coin in the elevator mechanism that happened a few years ago to a glider (no damages or whatsoever, luckily). At my club we had a passenger losing an earring while in flight and quite a bit of take apart followed....