Yes I meant something different. Generally with a load balancer the load balancer hosts that VIP(s) that your public facing DNS A records resolve to. In order to avoid a single point of failure you employ things like keepalived or ECMP/BGP etc.
The general setup seems to be that you have a public facing LB which just forwards all incoming traffic to any available fabio instance which handles the dynamic routing. fabio does not solve the public VIP problem for you.