What happens when an elderly parent doesn't qualify for Medicare and needs skilled nursing? Are the children responsible for payment?

I have posted many times here about my 90-year-old MIL who moved here 3.5 years ago from France. Her health is degrading and she has dementia, severe aortic stenosis, and recently fractured her c2 vertebra from a fall 6 weeks ago. She refused to wear the neck brace, literally pulled it off, absolutely would have nothing to do with it despite our warnings that the doctor said bones would shift and she risks paralysis if she didn't wear it. Fast forward, things did shift and the doctor now wants to do an anterior screw fixation for odontoid fracture to prevent paralysis. Some of you may recall that 8 months ago, we had decided against TAVR heart valve replacement surgery. She continues to smoke, and has a host of other problems including macular degeneration/ legally blind and is nearly deaf. Hard to have her be compliant when she doesn't wear her hearing aids most of the time.

We live in California, we do not have a lot of financial resources. MIL has ACA and does not qualify for Medicare until she has been here for 5 years. We signed a statement of financial responsibility in order to have her immigrate to the U.S. before she moved here. MIL has a pension from France and has been able to save money living with us.

If we can no longer take care of her in our home because she needs a skilled nursing care facility, I am trying to figure out what that means for us financially. She maybe has a couple of months of savings to cover the expense. But what if it's longer? Again, all this is hypothetical - I know my husband would do everything in his power to keep her at our home. Plus she does not speak English, making it difficult for any caregiver besides us unless they speak French. That being said, I could not do lifting or showering, and given her declining health and increasing difficulty doing things on her own, we would likely have to bring in caregivers/ nursing care at some point.

If she gets the neck surgery, is nursing covered post-operative under ACA/Obamacare for the short-term at home? The doc said that she would be released after one day at the hospital, and that it is a 1-2 hour procedure. BTW, all this has to be cleared by her cardiologist/internal doctor.

As always, thanks a million for your responses. I feel extremely sorry for her, I know it's really hard, but I am also completely wiped out from caregiving, not sure what to anticipate in the coming weeks.