Remember that spot, brother.
When they fall over, they often root(although it takes a few years like that sometimes) and THEN they pup from the end(s), sometimes in several places.
It is a technique known as using logs, I think.
One friend planted several 6" cuttings of bridgesii, sideways in the ground. In almost 3 years, his yield was way more than if he would have planted the 3' cacti.(close to 10' yield, he said. I believe, as I've seen the results with mine own eyes). And each of the places he cut, there will be one to three(or more) pups from there.
Anyways, that spot could produce many pups if there is some not ROTTEN. If any is good, it may root. Good luck.