If I understand your question, the answer is "yes". That is, mass and energy remain constant because not very much mass is "converted". The accounting of energy typically includes "potential" energy. This is a way of treating the energy as if it had not been converted into mass. Since the amount of energy is low, the mass change is extremely tiny and can be ignored. The potential energy term keeps the energy calculation in balance.
In most cases, "binding" energy is negative. That means that energy was given off during the binding and is missing from the bound particle. The potential energy of the bound particle is then negative. The bound particle will, I believe, have a mass which exactly accounts for this missing energy.
When a particle is created from energy, an anti-matter particle of equal mass is created. The mass of both of them convert into energy if they come in contact with each other, so I'd have to think that there has to be some potential energy in at least one of the particles (either matter or anti-matter)... When you say a bound (matter) particle has negative potential energy, I begin to wonder how any matter has potential energy.
I thought all matter *was* potential energy, where matter & energy have the ability to convert from one to the other, depending on externals. A particle with negative potential energy that you're talking about is making no kind of sense to me. What am I missing?
It is SO cool to read this scientific nerdy stuff and actually see people responding and discussing it. I think I am in heaven...
However, I am more a mathematics nerd. Can't wait for that thread to come along.