I don't necessarily think of stability when I think about the appeal of working for Fidelity. Their benefits are what keep people around.
I'm stuck in my current position - took whatever I could to get my foot back in the door. But even after earning my degree, the main thing recruiters look at is your current salary grade? Without even looking at outside experience before declining to submit you to the interview rounds.
I've repeatedly considered going to a different company, but the value I would be losing by leaving Fidelity is immeasurable. I would need to make at least $30,000 more to even equal the insurance and 401k matching they offer. That doesn't even address the $25,000 they have contributed to a Retirement Health Savings Plan that I would lose outright if I left.
And I've been there for 8 years now. I've seen repeated voluntary buyouts. In my experience the company tries to find somewhat more ethical ways of reducing the number of employees before they resort to layoffs. And again, layoffs usually affect the lowest performers.