Are there places, maybe private homes, that take people in for hospice care?

Most hospice agencies have hospice homes that their patients can use when the time comes. Medicare will cover the cost of the home 100% if the patient is expected to die usually within the week. If the patient lives longer than that, the patient has the option to leave the facility to go elsewhere, or can opt to stay in the facility and pay out of pocket. I can tell you if you pay out of pocket it will be more than you're paying now for the assisted living, by several thousand.
Your mom can be under hospice care in the assisted living facility she's in now as well. Otherwise like others have mentioned, you can look for a smaller board and care home in your area. Best wishes.

Hospice care is for people who are expected to live just a few more months. It's usually run by a company that has doctors, nurses, social workers, chaplains, and other employees to handle the person's needs, as well as their family. Unless your mother is in that condition, you aren't looking for hospice. Keep in mind, too, that hospice is largely paid for by Medicare, although it doesn't pay for the facility itself.

Look into board and care homes in your area. That's probably what you're looking for -- a small home setting for just a few seniors rather than a facility like you're paying for now.

You should google Board and Care Homes in your area. They often are family run and have perhaps 6 or 7 patients. For some they work out much better and seem more home/family like. They are often less in cost than ALF but not a whole LOT less. Remember you are paying for care, for housing and for food. I wish you good luck in your area. Use your search engine to look for such places in your area.