The term SUBSIST (ON) can be solved by the crossword solution of LIVE (4 letters). To subsist means to maintain or support oneself, especially at a minimal level. It is often used in reference to food, shelter, and other basic necessities. To LIVE is to exist or have life, and is often used in reference to people, animals, and plants. Therefore, to subsist (on) is to LIVE on something, such as food, water, or other resources.