I've had my employer essentially go bust twice, and left another company that was in dire straits but managed to keep going. It's all been fine, of course you need to keep your skills up to date but the idea that one employer going to the will is the end of my career is just daft. No.
Having said that I have had a close friend get his career badly derailed by health problems. That really sucked, but after some tough years he's back rebuilding his career and loving it. He's in the film and TV production industry and just loves what he does.
I think the moral is, do what you love and be good at it. I honestly have no idea what I'd do if I wasn't in IT, but I love the tech and I'm decently well paid, so it's all good. Not everyone is so lucky, for sure.