If you truly run out of money, then you are left up to what the state can provide.
I have many a relative that have gone down that path.
Housing: Assuming you exhaust everything selling the house. If you are lucky there is a spot in a section 8 housing type unit for elders. Ours has a waiting list of roughly 10 months. If you can't get in there, you will be forced to move up to 50 miles away to some other available housing which means you will not see or know anyone.
Food: Snap provides some, meals on wheels, food bank and honestly, you go to every single persons funeral,etc at church you know and eat the lunch provided. I've seen this as the primary way of eating in my town so they can save their money for meds.
Medical: You will get medical, a minimal amount of care, lots of prescriptions won't be included and you have to figure out how to get to/from the doctors which is often more of an obstacle in small towns than anything else. Often if you end up in the hospital, you won't be coming out or you end up at some shady rehab place where the recovering rates aren't good.
So basically you wake up everyday and your not dead. Your not suppose to have any money so you can't get a haircut, you can't afford toilet paper (as that can't be bought on SNAP), you barely have meds, you can't get from point a/b, and you may be living far away from everyone and everything you ever have known... but your not dead, homeless or starving which is the criteria. Basically you rely on family, friends and church to help provide any minute comfort in your final days.
Or you figure out how to work the system and its all good.
As for why do people get there.. well bad investments, spouses/agents that lie/steal from you, and just poor planning. Typically a spouse dies early and they didn't have proper life insurance or one spouse consumes vast amounts of assets in their final days leaving the surviving spouse penniless. People didn't read the fine print and realize the pension only was on the one person or the universal life policy you took out was basically fraud or the LTC insurance hosed you. And then there are all the people who never had anything, always lived in section 8 housing even during their working days so aren't going to magically have money when they turn 65/70/85.
My grandpa died at 56, was a farmer, had a tiny policy on himself, he left behind 10 kids, 9 of them under the age of 18, one still in diapers. Grandma died with about $30k left and it took a village to raise the kids, grown their own food, try to keep some income going on the farm until the youngest got older. Grandma then sold the farm, bought a mobile home, lived with one of the kids and did absolutely nothing so she wouldn't spend a dime.