> Why would the concept be at risk though?

Property—at least real, as opposed to personal—property seems to be unlikely to survive as a thing in the absence of civilization, even the species survives, and “civilization-ending” was the scenario being discussed.

> Will the species go extinct or would communists take over?

Well, species-ending would be compatible with civilization-ending, but not necessary to it. Ideological communism probably wouldn't survive the end of civilization, either; the problem it addresses would no longer exist nor would there be means to implement most forms of it, nor would any people that survived probably have much energy for theory.