Mum has Alzheimer's. Two weeks ago she fell and broke her hip. She came through the surgery fine but has now stopped eating.

You don't say how old Mom is.

Broken hips are very serious. Some elderly don't survive them. Your Mom really doesn't have any fat to rely on. Like said, going under is very hard on the elderly and mix Dementia into it ... When my Dad was going for a second open heart surgery, he mentioned to the dr. that he had memory loss after the first one. The doctor told him that was true. Dad was in his mid 60s then.

If she is taking liquids ask that she be given Boost at least. You may want Hospice to evaluate her. When the body starts to shut down, food isn't even digested or absorbed.

I think the answer depends on the age of your mother and how far along she is in her Alzheimer's, also on what other health problems she has. 90 lbs is frighteningly tiny unless she is very petite so even a few weeks of lower calories can be devastating, has the NH mentioned adding any high calorie diet supplements? I think you need to ask for a sit down with the DON and/or facility doctor to see where they feel she is at medically and what they recommend.

kaptagat, one has to remember that for every hour a patient is put under for surgery, it will take a month for the brain to get rid of the fog. Thus, if Mom's surgery was 2 hours long, she won't start feeling better until the end of two months.

I remember after having surgery, the last thing I wanted to do was eat because when I did, I felt very nauseous. So give Mom some time to recoup. Bland food works best, like mashed potatoes for a start.

Contact Hospice and they can help both of you through this.
Quite often with dementia surgery can be difficult.
First it takes a LONG time to get over the anesthesia. (talking possibly a month and even then not back to where she was prior to the anesthesia)
Then the rehab IF she is able to participate and many are not. So while the hip fracture is repaired there is still pain. (this makes everything difficult, including eating.)
Without surgery the life expectancy after a hip fracture might be 4 to 6 weeks with surgery it might be a bit longer than that but probably not much just due to pain and I am sure she is now pretty much confined to bed as placing her is a wheelchair would be painful.

I would say respect her wishes, if she is refusing to eat, continue to offer, and offer liquids like the enriched drinks, the enriched ice creams, puddings and the like. Once she stops liquids as well that will be very close to the end.
Keep in mind that WE associate food with all sorts of emotional things.
Love...I love you so I made you favorite dinner, I made a cake, cookies....
Wellness....Eat this soup it will make you feel better, you are sick so I made tea and toast.....
Sadness...I broke up with my boyfriend so I sat and ate a pint of ice cream..

But the body NEEDS food only as a source of energy. Once things start slowing down the body only needs to keep the heart going, the brain going. The feeling of hunger goes away. It does not need the food and it will not use the food if it is forced upon it so most likely the food will sit undigested in the stomach causing problems or it will be moved to the gut where it may cause blockages.
So if she is not eating do not force it,
Same with fluids and IV to provide fluids can cause problems as well.
Sorry I sort of rambled on with this but it is a topic I feel strongly about.
Again Hospice will provide you with help, education, support both emotionally and physically.

I’m sorry you’re going through this. It sounds like maybe your mom has had enough of this world. I’d respect her on this and not push the food. My mother’s doctors told us that the body does fine without food, but needs to be kept minimally hydrated to avoid the discomfort of dehydration. My mother had no food for weeks before she passed away, only small amounts of water. I fully understand the torn feelings you’re having, we’re never really prepared to say goodbye. If it is time, be sure to say everything you’ve wanted to say, hold her hand, and know you’ve done your best