Yes they could. It's always possible that another company could somehow do search or social networking better than Google and Facebook, find a really clever way of marketing their services and catch on before the former has any chance to catch up.

It'd help if either got much worse at their core business (since that tends to be what dooms a lot of companies nowadays), but even a strong Google could have a competitor that simply offers people a much better and more user friendly service.

But more likely is that they don't die to direct competitors. They die because they become irrelevant. Their 'true' competitor isn't another social network or search engine, it's something that completely replaces the need to have a social network or search engine.

For example, if a company came along and figured out a way to give people results based on what they were thinking about without any direct input required, that could make Google's typical search box and results page and ads completely useless. They'd be like a horse salesman after cars were invented. Same with Facebook.