Moving out of Illinois is easy. Stopping Illinois taxes is a different act, and it happens on paper: Illinois keeps treating you as a resident until the record shows otherwise, and the burden of showing otherwise is on the taxpayer asserting the change; only one domicile at a time.
There is no day-count to get under. Illinois defines a resident as anyone in the state for other than a temporary or transitory purpose, or domiciled in Illinois but absent for a temporary or transitory purpose. There is no fixed day threshold — the facts decide, and temporary absences expressly include wintering or summering out of state. That makes the evidence trail — where the pattern of an actual life points — the entire case. Everything on this page exists to answer one question: if IDOR asks, does your record hold?