a thousand? no. a few hundred, sure.
lower GMs

well, if you are say, 2600 at your peak but now you're 80 years old, i think you could easily play at the 2300 or 2400 level. not saying that happens a lot, but it's conceivable. at least, more conceivable than going from 2600 to 1600. :D

losing a big tournament could cost you a hundred or 2 but x10
It is mpossible to lose a hundred points in one tournament. Here is the FIDE Elo calculator http://ratings.fide.com/calculator_rtd.phtml
Say 6 GMs are in a closed double round robin tournament and for simplicity everyone is rated 2600. Each loss costs 5 points. Someone loses all 10 games that is 50 points.
Say it is an open nine round swiss and starting off with a game against a player rated 400 points or more lower. The maximum for ratings purposes is 400. Careful with the calculator it allows a more than 400 difference.
http://www.fide.com/component/content/article/1-fide-news/4059-changes-to-title-and-rating-regulations-effective-from-july-1st-2009
A loss to that first player costs 9.2 points. Say after the first loss it leads to all opponents 400 or more points lower.
9 losses times 9.2 = 82.8 (One reason you see only Ivanchuk of the big players in opens.)
have some GMs forgotten chess or decrease in rating by a thousand