Not exactly sure how they do it, but here is plausible explanation.
Some ISPs allocate static IP addresses dynamically based on the username. So I suspect if the primary link goes down and the second dials, then it gets the same ip address.
Let us know if you find out how they do it...I am asking because they may use something like ip unnumbered loopback0 with the backup command etc...not sure how it will work with NAT...