Mother has dementia. Can she get government assistance and keep her house?

I am a lawyer in CT and practice in this area of the law.  You are dealing with what is known as Title 19.  Under this statute, the state will pay for your mom to be in the nursing home; however, the state will not pay for the nursing home services unless your mom has no money or assets.  the fact that your mom owns a home, the state will not pay for nursing home services up to the amount of the equity/assets  that your mom has.  the state looks back 5 years to determine the amount and extend of the assets.  In short, you mom needs to sell the home to pay off the debt.  if there is money left over, then that money will likely be the amount of money that the state will look to obtain to exhaust before it will pay for your mom to be in the home.