Static Structural is solving the matrix equation: [K]{u} = {F} and during assembly of the stiffness matrix [K], if the supports are not present, the matrix is singular and there is no solution.
Transient Structural is integrating over time a different equation: [M]{a(t)} + [C]{v(t)} + [K]{u(t)} = {F(t)} and in this equation, you can have zero stiffness and the equation reduces to {F(t)} = [M]{a(t)} if you ignore the damping matrix.