Energy is a concept for which only the differences between two well specified situations play relevant part. Force, for instantce, is defined as the spatial derivative of energy, which clearly means that global addition of a certain fixed amount of energy will cause no physical result.
Nevertheless, as we can always sum a constant value to the energies of all positions (potential energies in the case of a conservative field) we may, for convenience, decide to attatch negative values of energy to those situations where the particle is confined and positive energy to non confined states.
Therefore, if in a pure gravitational situation, a particle have total energy negative, then it means that there will be a moment where all the energy will be in the form of potential energy due to gravitational force and the it will be at rest and/or at a limited distance from the gravitational center.
But if the particle have zero or positive total energy then, even subjected to the gravitational pull, the particle will be likely to be observed at arbitrarily great distances from the gravitational center.
In short: negative energy is just a matter of convenience to represent confinement. You can always redefine it to set some negative value to positive or zero.
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