My mother is in an Assisted Living facility. They now tell us they are increasing her rate 10%. She can barely afford this already!

Read any contracts you signed.
In general, yes, it is legal. Especially if care level has increased at all (Level of Care). Usually the norm is increases of 3% to 5%, but inflationary costs are dreadful, and anyone buying food and sanitary supplies now is well aware of this. That says nothing of staff which often is on overtime due to illness of other staff, and demanding increases in pay due to being on the front lines. I am afraid inflationary costs in the country will hit the elder community very very hard.

While that's a lot, I agree with another post that this is probably part of the inflation we are experiencing now.

Can she afford the increase? Will it just spend down her money faster?

I'm not sure how advanced her dementia is. Or how long you expect her $ to last. But when her condition warrants MC/SNF or she is running low on funds, it might become time to look into where she will live next and ultimately have to go on medicaid.

Check her contract. Rates go up annually. Rents for apartments food costs have gone up dramatically due to inflation. NH’s are no different than expenses in all other segments of the economy.

Read her contract. The rate will go up on a yearly basis for her room and board. Also for her care which was separate from her room and board. As her care needs increase so will the cost. So what is the increase for? If rent, then I would question. It is a residence and may fall under the State laws in how high can rent be raised.