The rules are the same as when Eagleton dropped out in 1972. The DNC picked a replacement. But the Eagleton situation and replacement was a disaster, and the Democrats know it. Biden is in it till the end, and nobody is even thinking of replacing him. Both candidates have their running mates and both are stuck with them.
http://www.nashvilleistalking.com/node/67916
I am not sure of the Eagleton situation, but was he already officially nominated when they tossed him overboard?