Parachutes made from silk were certainly about by WW2, One of the primary issues to come was that this material was sourced from Japan which dried up as the build up to war gained a momentum.Which is where yer Nylons (New York/LONdon) and Rayons came in for the allies.
Very early on silk could still be found - doubtless starting more stories than actual examples. I recall my mum being ahead of the plot of a Dad's Army episode wanting to check the colour of Warmington-on-seas knickers due to German ones being cream and allies being white (IIRC).
Can't remember where I read about a German parachute being found and retrieved, locals keeping quiet and later on realising the user had gone into soft ground.
That'll be an interesting bog body if found.