It's called the FOD Walk or foreign object damage. I've done it on occasion on the LHAs. Someone yells down to the berthing area "turn out for fahd walk!" Sometimes over emphasizing the faaaaaaaaaaaaahd waaaaaaaaaaalk. very annoying.
Finally - somebody called the name FOD Walk. Also in general you are correct.
About Russian jets - the Su-27 and MiG-29 (old ones) have the "FOD Screen" but in general they are dropping them like in MiG-35 and MiG-29M or their stealth Suchoi. In general the Russian engines are more prone to FOD, also another problem rather the Russian runways that in generally has lower quality maintenance.
About runways being destroyed - if it is destroyed the FOD is the "lesser" problem - first you need to close the holes. And today everybody does this efficiently (everybody learned the 1967 6 Day War lessons)