In the ordinary course of events, parents are allowed to not support their children in college.

Separately and unrelatedly to my sibling comment, I note that while parents are certainly "allowed" to do this (in the sense that they have the legal right), many people consider this not a very decent thing to do.

The law seems to agree. State-funded grant programs (in at least some states, certainly including New York at least), as well as federally-funded grants, calculate your eligibility for need-based aid on the assumption that your parents will support you if they are financially able to do so (up to a certain age of the student — I believe NYS puts that cutoff at 27 years of age).