Conservation of energy is a fundamental building block of physics. If electromagnetic radiation is not absorbed, it will continue to propagate, and on opening the box, the same radiation would escape.
The idea of "cancellation" of electromagnetic waves is ingrained into us at an elementary level of science education, but it's almost never taught with a full flavor of the complexities involved with this concept. In general, circumstances which are normally described as "cancellation" are better described by the idea of "alteration of propagation". Noise "cancelling" headphones, for instance, sample an incoming (practically planar) wavefront and issue an expanding spherical wavefront of opposite phase and similar amplitude. This mutes the propagation in a narrow cone from the cancelling speaker along the direction of the original planar wave, but adds ADDITIONAL energy to some other directions, where cancellation does not take place.