I work at a company that I think is probably big enough, and in a safe enough market that it can't fail. It might not keep up with its peers but competition in entrenched industries makes it hard for a company to fail once they become entrenched. Kind of like barnacles on a ship. The worst that could happen (from an employee perspective) would be being acquired, with the resulting consolidation eliminating redundant jobs.
And many companies are like this. I joke that when our company is trying to make a decision, the first (and often only) thing the executive team asks is "what are our competitors doing?"