I don't have a crystal ball, but I'm betting that someone buys Remington at some price at some point. We may well see no new guns produced for a short time, but at least some of the basic designs will be back. The 700 may be gone. There are already several companies making actions based on the 700 that have improved on all of the 700's shortcomings. I'm not sure even an improved 700 would be able to compete. There are better semi-auto shotguns, but I'm betting someone keeps the 870 alive.
Ammo and components I don't know about. Even if the firearms side goes away and doesn't come back I'm betting the ammo part will find a way to continue. Winchester firearms, and Winchester ammunition split into 2 different companies years ago. I'm thinking 1970's. There is too much demand for ammo right now, and for the foreseeable future to stop production.
Winchester closed the doors to the New Haven factory in 2006 and for the better part of 2 years no new guns were made. FN bought the company and started limited production of a slightly redesigned model 70 in 2008 in their South Carolina factory. Some of their rifles are made at a factory in China and at least some are made in Asia. Some were never re-introduced.
I'd expect something similar with Remington. But to be honest this is all speculation.