If every member of an estate dies, does the private road go to the township?
First, you will need to look at the documentation (if any) which created the private road. It might indicate what happens in the event of death.
If there is no clear indication, typically private roads belong to one or more landowners. They are usually created by an easement which “runs with the land,” meaning that whoever owns the land owns the road, too. So the question then becomes who owns the land?
Even where an owner and all of their descendants have died, it’s rare for an estate to pass to the state (“escheat”). Most states have a fairly long list of potential heirs who come first; you’ll need to check your state’s laws and maybe do some detective work to figure out who stands to inherit. This is assuming the prior owner doesn’t have an estate plan, which of course would override any legal defaults.