Can they kick her out?

It is heartbreaking to think of an older adult in serious need of care being thrown out. I can’t imagine this happening to anyone. Where would they go? Family members aren’t equipped to handle their loved ones who have these challenging conditions.

Speak to the DON at the nursing home and express your gratitude to them for caring for your mother and say that you don’t know how you could possibly manage caring for her at home. Do ask them what suggestions they have for preventing these falls from occurring again.

I think that you will be able to put your mind at ease knowing that they will hold a spot for your mom at the nursing home.

Wishing you and your mom all the best.

My Mom had a Geri chair. It looked like one of those flat slat vinyl beach chair with wheels. The seat could be slanted backwards so makes it hard to get out of. Also reclined so Mom could nap in it. There were cushions on each side of her head to keep her head from slouching over when she slept. She scooted all over in it.

There are ways to slow a person from getting up out of a chair or a wheelchair.
If a wheelchair you recline it a bit, tilting the back a little. This makes it a bit more difficult to get out of the chair.
If she is in a regular chair reclining it a bit will also help and adjusting it so it is not as easy to get it upright. (my daughter used to direct my Husband into a rocker recliner chair that they had he could not get out of that chair until someone helped)
Placing a chair alarm helps but it can be disruptive.
Placing a chair right up against a table will slow someone down. Trying to get out of the chair you have to push it back and a movement like that should be noticed by staff.

There is also the great possibility that the broken hip will definitely slow her down and depending on how she does in rehab she may be past the trying to get up on her own.

When you say NH are you actually talking about a Nursing Home AKA a Skilled Nursing facility or are you talking about Independent Living facility or an Assisted Living facility?
Generally Independent Living will not have staff come and help residents. So if mom is falling or depending on staff to help her then she really is not "Independent' and should probably be in Assisted Living.
If she is in AL and is not waiting for the help to arrive they may determine that she is a danger to herself and needs a higher level of care. They may not "kick her out" but they may suggest either Skilled Nursing or Memory Care. (is there a diagnosis of cognitive decline or dementia that might make her living in independent or Assisted more of a risk?)

Generally this is the type of patient that nursing homes in general do deal with. I cannot imagine that they would "kick her out" because of illness and falls, as I would imagine they have few who are not dealing with these situations in their care. That doesn't mean they will hold a bed for a month she will likely be in rehab.

If you signed a contract you may want to read your entire packet. They often state the reasons someone may be asked to leave.

The important thing for you is NOT to start upsetting apple carts at this time. Your Mom is going to need at least a month of time for rehab I would think. They are unlikely to "hold a bed" but they are likely to take her back if they have a bed, and I would assume that is the case.
Do not contact them until they contact you.
And once Mom is better it is important that you not accept her into your own care and home, even "temporarily" (because it won't be): not even with promises of "we can get you help " (they can't) and "we can make this work" (they won't).
Make certain that you let them know at discharge planning time that you are in no wise able to take your Mom into your care EVER even temporarily--not physically able, not mentally able, not emotionally able.
They will then have to find placement at her current facility (preferred) or a new one.

Good that you are thinking about it now. Mine waited until the day my Daddy was released from the rehab to tell me they would not take him back! grrr! Keep in talking with the administrator so that you know where you stand. I had to put my Daddy in a group home and let me tell you that was better than the memory care facility that he left. I was treated like family with them and the communication was soooooo much better!