Not a question of much historical significance, but when thousands of troops parachute into a battlefield, what happens to their parachutes? My grandmother used to tell stories about silk stocking shortages in WWII -- surely the silk was just as valuable where the soldiers were landing? Were they collected?
The troop parachutes used in training jumps were almost always repacked and reused (unless they were too badly damaged). Troop parachute like the American T10D design used during WWII were usually durable enough to be reused several times.
In combat, parachutes were rarely recycled. Paratroopers ditched their primary and reserve chutes immediately after landing. Fighting, not salvaging parachutes was the priority of airborne troops. Some soldiers did keep parts of their parachutes for personal use. Improvised silk scarves made out of camouflaged parachute canopies were a popular item of dress for some airborne troops. One soldier, 2nd Lt. Harry Welsh, even saved his white silk reserve chute for his fiance to make into a wedding dress!