SelectNotFree[expr, x] returns that part of expr which is not free of any occurrence of x.
SelectNotFree[expr, a, b, ...] is equivalent to Select[expr, !FreeQ2[#, {a, b, ...}]&], except the special cases: SelectNotFree[a, b] returns 1 and SelectNotFree[a, a] returns a (where a is not a product or a sum).
SelectNotFree[a + b + f[a], a]f(a)+a
SelectNotFree[2 x y f[x] z, {x, y}]x y f(x)
SelectNotFree[a, b]1
SelectNotFree[a + x, b]0
SelectNotFree[a, a]a
SelectNotFree[1, c]1
SelectNotFree[f[x], x]f(x)