It's never absolutely guaranteed, but it's not like it's some phantom principle. With a bit of awareness, in most cases, you should be able to predict the likelihood that your position at your present employer will continue to exist (and the likelihood that your employer will continue to allow you to fill it).
Nowadays more so, but back in the day it was a more stable job environment.
That said, while nothing is 100% certain, there are jobs and companies that are more stable than others. Even in trendy companies, not just IBM-style monoliths. You don't often here about massive layoffs at Apple or Google, do you?
Speak for yourself. I have 2 teenage daughters, healthy savings, and I'm under 40. It takes discipline and a plan. Dave Ramsey ( http://www.daveramsey.com ) helps as well.
I have two toddlers, a third on the way, and no savings. I have discipline and had a plan (and had savings). The plan went wrong.
For the time being I do have job security and it is what I need at this stage in my life. That will change (hopefully), but the 9-5 is a godsend right now.
Plans and discipline don't have guaranteed "security" either, so beware.