The "family" talk is only just talk. If an employer says "we're family here" or some similar nonsense, it's not family as in "we stick together through everything" - what a family actually is or should be.... It's more of a farengi perspective...
Rule of acquisition 111: "Treat people in your debt like family… exploit them."
And rule 6: "Never allow family to stand in the way of opportunity." (Which is also cited as "Never allow family to stand in the way of profit")
Fact is, they want you to be family in the way that you'll do anything for them, like you would for your own family. But when it comes time that you need them to help you out like a family would, they'll show you the door very quickly.
Related: if you're hit by a bus tomorrow, your job will be posted before your obituary. You're just a cog in their money printing machine. As soon as you lose your value in that regard, you're gone. If you slow down the machine too much, they'll find a cog that is more easily lubricated (to push the analogy). If you're broken and can't work, they'll replace you without a thought. Management is there to put a nice face on the company (for your benefit) and make it seem less like you're a number; but that's all you are.