What is the point of EFC if the family cannot meet it??

My sister has many emotional special needs and going to a big, cheap state school or community college would be too “traumatic” for her. The only money in my college fund is 20k, the only “real” money allocated for me. My family is going to try to pay for me through “hypothetical” money, which is the key issue here. They are willing to pay wherever I go, but I need to save as much money I can for medical school.