First of all, it is important to note that I'm not very savvy in neither general relativity nor any other area of expertise that answering this question may require. Therefore, I mean for the question to be answered in layman's terms.
Okay, now to the question itself: as far as I understand, for a given energy total in a system, its contents can theoretically be put into any other configuration of energies with the same total sum (if that makes sense). Therefore, if that sum is zero, the contents can be configured into, basically, 'nothing', which also has an energy total of zero.
However, with the universe, the only sources of negative energy are the fundamental forces. I think it may be reasonable to put all forces other than gravity aside, as only gravity is generated (sorry for funky wording) by something which itself is another source of energy (mass), and all the other forces eventually cancel out. If we also ignore the dark energy, we are left with a collection of masses that will eventually crunch together. Here is the problem I have with this: where will the mass go? Even if the potential energy of every point in the universe is zero (i.e. all the mass in the universe has now been smushed into a point), there is still mass to deal with, right?
I know I am probably wrong in many, many places in this question, but can you explain the general, underlying flaw behind my reasoning?