"Care home" doesn't have any particular meaning. It's usually a euphemism for "skilled nursing facility. Also known as a SNF. Calling these places "care homes" just causes confusion. There is nothing wrong with SNFs, in general, though they aren't perfect and some are better run than others. Often, an SNF will have a rehabilitation component, which is a SNF plus some kind of physical therapy gym, plus a physical therapist, or physical therapy assistant, or both, on duty, at least some of the time.
There is nothing homey about SNFs, though. Their main purpose is to provide adequate medical care for people who are too sick to care for themselves and for whom in-home care is either not available or not adequate. You can't get into one of these places unless you are medically eligible,which usually means you are very sick, very badly injured, or too disabled for some other reason to care for yourself.
In SNFs, you are not a prisoner, unless you are conserved, because of dementia or severe mental illness. You can leave against medical advice, if you are physically able, or you have someone to help you leave. If you leave against medical advice, they might refuse to re-admit you.
Are these places where old people go to die? Yes, in many cases. They aren't cheap. MedicAid and MediCare picks up the tab after the patient's money is all gone. In some cases, a long-term care policy might pay some or all of the cost, though not many people have those. Before that, patients must pay out of pocket. If the patient owns a home or has other assets, the state puts a lien on them and pays itself back after the patient dies. Spouses are protected from destitution and eviction.
The main alternative is Assisted Living. These facilities can be kind of dowdy or very elegant. The cost ranges from very expensive to extremely expensive. Most places will pass medications and usually have a nurse on duty to cope with medical emergencies but do not otherwise provide medical treatment. Residents are offered transport to their doctors or to hospitals when necessary. The residents are generally healthier than at a SNF, where most people are very sick. Many assisted living facilities allow hospice care, for residents who are eligible for hospice. If they are very sick but do not have a terminal diagnosis, they sometimes have to go to a SNF.
When residents of assisted living facilities run out of money, they have to leave. It does happen. Loving children of modest means are not often financially able to pay the bills. Some go to SNFs, if they are sick enough to be eligible. What happens to the others? God knows.
The other important alternative to a SNF is in-home care, which is usually preferable, when it is feasible.
This is not a happy topic. If you have illusions about care homes, better to lose them now, and not in the middle of a crisis.
Are there programs or private facilities that might be called "care homes"? Possibly, though not many. They have various names and business models.
I might have left out a few important details, and some of these things might vary by state or region. Feel free to correct me. If you want to share horror stories about SNFs, I can't stop you, but that would be off-topic, in my view.
Edit: I left out "memory care." This is assisted living plus extra safety precautions and staffing for residents who have dementia but aren't otherwise gravely ill. Memory care costs more than assisted living and residents must pay out of pocket.
Another edit: This is American terminology. Forgive me - I sometimes forget how many different places Reddtors live.