According to the answer of @PhysicsDave here, there can be energy stored in an electromagnetic field even when the $E$ and $M$ fields are zero everywhere.
However, according to Griffiths, page 380, equation 9.53, the energy per unit volume in an electromagnetic field is given by $$\frac12\left(\epsilon_0\mathbf{E}^2+\frac{1}{\mu_0}\mathbf{B}^2\right).$$ So when $\mathbf{E}=\mathbf{B}=0$, this would equate to zero.
How can this contradiction be explained?
If standard Poynting expressions for EM energy are adopted, then vanishing fields $\mathbf E,\mathbf B$ in vacuum indeed imply zero EM energy density there. So in this context, PhysicsDave is wrong.
Although PhysicsDave did not explain what he means, his statement could be true if non-standard expressions for EM energy density and EM energy flux vector (other than the Poynting expressions) were adopted (which is entirely consistent with EM theory).
Density of EM energy $\rho$ and vector of EM energy flow $\mathbf S$ are ambiguous, because they are defined based on the desired equation form
$$ \partial_t \rho + \nabla \cdot \mathbf S = -\mathbf j\cdot \mathbf E $$ which does not fix exact expressions for $\rho, \mathbf S$.
One possible set is the Poynting set, but given any pair of functions $\rho, \mathbf S$ which obey the above condition, we can define another pair via
$$ \rho' = \rho - \nabla \cdot \mathbf u $$ $$ \mathbf S' = \mathbf S + \partial_t \mathbf u $$ where $\mathbf u$ is any vector field differentiable in both space and time coordinates. With a convenient choice of $\mathbf u$, and using Poynting's expressions for $\rho,\mathbf S$, we can get non-zero $\rho'$ even in places where $\mathbf E = \mathbf B = \mathbf 0$.
If you are letting (M) represent the magnetization within a ferromagnetic material, it might be possible for a superconductor to maintain a (B) without an (E).
