I have a friend who knows a lot about the phone system (he has a security clearance for some of his telephone work). One time we had a long conversation about this topic, until at one point he said "and let's talk about something else" -- I guess from that point some of the details are classified. So maybe there is a plan, or maybe they just designed the system in such a way that they could convince themselves that it would not go down unless things were so severe that loss of the phone system would not be your chief worry.
---
In September 2001 there was a full standdown of US airspace. That was accomplished pretty quickly: "you are ordered to land immediately on the closest airport that can handle your aircraft, or be shot down". Undoing that, however, took some careful planning! Fortunately the standdown lasted several days so there was time to work it out. Even if you had a plan for this (and I assume FAA had one), figuring out what the realities on the ground were and matching them up with the plan was nontrivial.
Apparently some of the planes landed where they could not take of again unless they were empty with a small amount of fuel to get to an airport designed for them. I don't believe I heard that any planes landed where they could never leave.