The frame in which the net momentum of a system of particles is zero is the proper frame for that system, by definition.

The original question stems from a long-running debate at two other forums regarding mass-energy "conversion." Mass cannot be "converted into" energy any more than length can be "converted into" the components of a radius vector. When a bomb detonates, the mass of the system (including the ejecta) remains the same. Chemical or nuclear energy becomes kinetic energy, but that is all that happens.