For each destination, an EIGRP router also calculates a Reported Distance (RD), aka Advertised Distance, for the neighbor advertising it. It is actually the metric to the destination seen from the point of view of the neighbor. This will be lower than the metric calculated by the router.
All routers that advertise a RD lower than the FD for each destination, are called Feasible Successors. These routers, are guaranteed to have a loop free path to the destination. EIGRP achieves quick conversion by immediately using one of the FS routes as the new Successor, in case the path via the Successor is down. All other paths cannot be guaranteed to be loop free and are not used in this step.