Well, there's no such thing as the "velocity of an electron moving around a nucleus." The physics of subatomic, atomic, and, to some degree, molecular particles is dominated by quantum mechanics. If you measure the velocity of an electron, then it can not be localized to the vicinity of a nucleus. If you measure the position of an electron, then its velocity can not be determined. This is known as the Heisenberg Uncertainty Principle.

The "particle", or at least the ability to make measurements about the particle, is probabilistic. In the Bohr interpretation of Q.M., the probability function IS the particle. It exists every where with certain odds of being at a particular place. In the Bohm interpretation of Q.M., the probability function describes the odds of branching between universes, popularly known as alternate realities. These two interpretations are mathematically equivalent, and both allow for a small, but finite, probability of particles, or a field associated with the particle (gravity, information, etc.), to at least appear to travel at, or exceed, the speed of light.

That said, I presume you are envisioning a mass being accelerated nearly to the speed of light. Assuming the mass survived the mechanical stresses involved in the acceleration, it will not "dissolve" into energy. In fact, in the mass's frame of reference, it is you, the observer, that is moving nearly at the speed of light. Neither you nor the mass "dissolve" just because you're moving RELATIVE to one another.