The easiest way to do this would be to have a secondary route in your routing table with a higher administratie distance than what you primary route is. For example, is subnet 192.168.2.0/24 is at the remote site connected by the E1, and you are running EIGRP as your routing protocol, your routing table would have an entry of:
D 192.168.2.0/24 [90/2195456] via 192.168.1.1, 4w5d, Serial0/0
You would need to have a route that points to your VPN with a higher AD that EIGRP which in this case has an AD of 90. The easiest way to do this without introducing a second routing protocol would be to use a static route. This would look like:
ip route 192.168.2.0 255.255.255.0 10.10.10.252 91
In this example,, 10.10.10.252 is the next hop to get to your VPN and the 91 is the value set for the AD of this seconddary route.
Once the EIGRP learned route is removed from the routing tables due to link failure, the static route will then be inserted into the routing table and traffic will be routed according this next hop. Once the E1 link comes back up and the route is learned via EIGRP again, the EIGRP route will be installed back into the routing table the the static will be removed from the routing table.