The paratroopers would be stuck behind enemy lines, given orders to surrender as the operation failed. The paratroopers dropped at night before the landings and had objectives to complete before the landings. If the landings failed they knew they would be stuck. 18,000 paratroopers at the time of the beach landings were behind them, disrupting German artillery and securing key bridges. The paratroopers though were supposed to be resupplied from the air, these supply planes often got disrupted crossing German territory (Especially in the day). These were short-term re-supply missions not capable of sustaining an attack from the Germans from almost every direction supported by tanks,artillery and mortar fire.
They were to be marginally reinforced by Canadian and British glider regiments but the bulk of the reinforcements were to come from the beach. The paratroopers would have been disorganized, drastically running low on supplies and suffering too many causalities. A rescue mission was not possible, the amount of wounded suffered during the drop was to much to handle. Once the Germans had repelled the beach landings they would have re-organized and crushed the remaining paratroopers.
I would also like to attribute the successful landings at D-day to the Americans learning from their mistakes in amphibious landings during the African Campaign with their landings there.
Fleming, Thomas. "D-Day: The Great Invasion"
Buckingham, William F. (2005). D-Day The First 72 Hours
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growing up I was told that my Grandad paratrooped behind enemy lines on D-day with the British Army... he also apparently got shot in the head during this mission but survived. I only met him once and I was little, so I didn't ask. I've never been able to confirm how much truth is in this story as a lot of these kinds of things get embellished. I was wondering if anyone would know the best way of figuring any of that out? like whether he at least was part of the operation at all?