I've also seen people make careers out of taking over projects cut for the above reasons as customers still demand support. I've seen many downturns where my project was important enough to not be cut.
I've seen many downturns where my project had massive cuts, but I personally was not the person cut. Most often projects are not killed outright, instead they go through a long down spiral (not always, but typically) and you can make a lot of money being the expert on a product that is making money if you are able to hang on. Someone needs to leave as there isn't the budget to pay everyone, but that someone need not be you. Often these projects pay very nicely for working 9-5 with no pressure to do overtime.