Not sure if the rules are the same in softball and baseball, but this actually happened here in Ellensburg (2009). In a game versus Central Washington University, a Western Oregon player hit a homerun (the first of her career), and in her excitement tore her ACL when she missed first base. She collapsed to the bag in a heap, and the ruling was "a two run single" if she was unable to make it around the bases. Unable to be touched by teammates, she was then carried around the bases by CWU teammates Mallory Holtman and Liz Wallace.

Here's the short ESPN documentary, great sportsmanship:
https://www.youtube.com/watch?v=UEDBnKahuNs

As for dropping dead BEFORE reaching first, I have no idea.