If you're poor and sick, you get treatment, and you might end up in one of the following situations: 1. You fill out financial hardship paperwork, have most of the cost written off, have a small debt to pay off, 2. You fail to fill out financial hardship paperwork or aren't quite poor enough to get the cost reduced much, you pay it off slowly over time or file bankrupcty.
I've been in both situations when I didn't have insurance. Economically, it would be much better off if we had universal health insurance, so major sickness wasn't so crushing economically, but we don't "just die".
What is true is that people die sometimes because they don't have insurance and can't afford preventative treatment for conditions they don't know about until it is too late.