How do you get someone who has severe Alzheimer's to eat when they angrily refuse?

If a person is hungry enough they will eat, if they are able to safely eat. Leave the food on the table, could be the person thought they had already eaten and isn't hungry for the next meal. Alzheimer's can trick the mind.

Have you noticed if the person is coughing while eating? If yes, it could be the food isn't going into the stomach but into the lungs which can eventually cause bacterial pneumonia.

They can go a long time without solid foods if they will still take liquids. Throw an egg, a banana, a scoop of ice cream or frozen yogurt and a half cup of liquid vanilla creamer into a blender. Liquefy it. Serves you and him.

By severe do you mean end stage, or are you just referring to severely dysfunctional behaviours? There are lots of ways to pack calories and nutrition into soft foods or liquid diets, so the brief answer to your question is that they could live this way indefinitely.

Refusing food at the end of life is part of the final progression of the disease, as muscles atrophy and organ function declines they lose their appetite and no longer want or need much food, eventually many will refuse to eat altogether.

If you mean they are being difficult but are not at the end of life stage then you will need to investigate to see if you can discover why they don't want solid food. Do their teeth hurt? Are they having trouble swallowing? Are they plagued with indigestion? Or are they just behaving like a toddler who only wants to eat their favourites?