I think that it's unlikely that UA will drop all of its South American service unless things go really badly in the bankruptcy proceedings. Indeed, with the recent announcements that it was discontinuing flights to CCS, SCL, MXP, DUS and AKL, UA clearly hasn't been reluctant to drop its service if it thought that the markets couldn't be made profitable in the near future.
As to the U.S. departure points for United's South American flights, I think that we will see more nonstop service from the carrier's hubs, especially IAD and ORD (and perhaps even LAX at some point), while the MIA nonstop service will basically remain static with the two primary and historically very profitable markets of GRU and EZE, with the possibility of GIG nonstops returning if traffic improves again.
It will also be interesting to see how the new IAD-GRU/EZE nonstops perform. If they do well, it might encourage UA to add some other nonstop destinations from IAD. For instance, the local Washington (all 3 airports)-LIM market is substantially larger than either the Washington-GRU or Washington-EZE local markets where nonstop service now exists, with most Washington-LIM traffic currently connecting via MIA and, to a much lesser extent, ATL. The ability of UA to flow traffic from the Northeast and Upper Midwest (and even a few European cities) through its IAD hub, combined with some fairly decent-sized local Washington markets, could make IAD a major gateway (after MIA and JFK, of course) to South America. JMHO.