I've had a jack stand break before, and nearly take my hand off in the process.
We all need to stop buying cheap jack stands. That $200 ratchet is a pointless purchase if you're not willing to fork up a good amount for jack stands. It's idiotic.
Buy from someone who makes them properly in a nation that's respectable; a place that is willing to prove their stands can take the weight, and a place that welds them well.
Don't get them from Autozone, NAPA, Sam's, Tractor Supply, or anything of the like. Buy good ones, because their purpose is not only convenience; it's to save your life.
You should certainly place a tire or blocks down there if possible to catch the car if something breaks, but that's not always reasonable. You need to have quality jacks and stands before breaking the bank on all that cool chrome in the tool box.
It's just like photography. Don't buy an expensive camera until you have a very good tripod. The cheap ones may work, but they don't cut the mustard when it counts, and they're an irritation anyway.