Multiple IPs was one solution, but the other was much simpler.
The real address of the computer was its MAC, the prefix simply said how to get there. In the event of a failover, the client's computer would be notified the old prefix was now transitory and a new prefix was to be used for new connections.
At the last common router, the router would simply swap the transitory prefix for the new prefix. The packet would then go by the new path.
The server would multi-home for all prefixes it was assigned.
At both ends, the stack would handle all the detail, the applications never needed to know a thing. That's why nobody cared much about remembering IP addresses, because those weren't important except to the stack. You remembered the name and the address took care of itself.
One of the benefits was that this worked when switching ISPs. If you changed your provider, you could do so with no loss of connections and no loss of packets.
But the same was true of clients, as well. You could start a telnet session at home, move to a cyber cafe and finish up in a pub, all without breaking the connection, even if all three locations had different ISPs.
This would be great for students or staff at a university. And for the university. You don't need the network to be flat, you can remain on your Internet video session as your laptop leaps from access point to access point.