Be, exist, live, subsist are comparable when they mean to have actuality or reality.
Be applies to whatever has a place in the realm of things describable as real in a material or immaterial sense; only its context makes clear whether it asserts physical or spiritual reality.
Exist adds to be the implication of continuance in time; it also commonly implies a place in the realm of things which are describable as entities or as having independent, objective being.
Live basically implies existence in the realm of things possessing the character called life, which distinctively characterizes plants and animals and is manifest especially in metabolism, growth, and reproduction.
Live, however, is often applied in an extended sense to immaterial entities (as ideas or beliefs); in this use it may carry a suggestion of qualities associated with life (as persistent existence, vigor, activity, and development).
Subsist may be used in place of be, or exist, or live because it may imply the kind of reality or actuality connoted by one of those terms, but it (or more particularly its related adjective, subsistent) often additionally suggests a relation to or dependence on something; thus, a thing that subsists by itself (a self-subsistent thing) is independent and selfcontained; an idea subsists or maintains its existence only so long as it appeals to the mind of thinking men.
In philosophical use subsist is used often in reference to purely mental conceptions and implies logical validity or the character of being true or logically conceivable.