If they respond now to low prices by cutting production, they will lose market share, which is not something cartels normally want to do. But if they hold their nerve they will retain what they have. Low oil prices tend to increase demand (obviously), I read somewhere that a $20 fall is equivalent to a $2 trillion global stimulus package, which can't be such a bad thing. In the meantime it can be seen as Saudi Arabia's contribution to sanctions against Russia and Iran - and much more effective than our sanctions against either.
Plus they will deter investment. Not so much in American shale - which is still largely dominated by drilling companies which operate as annual partnerships; so they borrow money at the start of the year, and return all assets and income to the partners at the end of the year. They can scale their investment according to prices very quickly. Shale drilling will probably tail off a little in a few months, production should be down within a year or so I would assume. But it can spin up again at the drop of a hat.
Petrobras cannot do the same for the giant terminals they need to build to bring to shore oil drilled from beneath miles of water followed by miles of salt off the coast of Brazil. They will have difficulty finding funds for those projects though. The Russian Arctic is similarly a big, risky, and long term investment. Argentina has theoretically huge shale reserves that it can't exploit without roads and pipelines, and maybe Mexico too. These, and other threats can probably be made to go away for a long time if the output price looks [LIFTED].
A couple of years ago there was a video doing the rounds of some scientist bloke explaining how we can never have cheap oil ever again by the way. I wonder if he's penniless yet.