It could be a property of space-time, as space is always expanding everywhere, space it self could have a negative mass.
This could even be some sort of weird energy-neutral balancing mechanism (e.g. some sort of energy - my bet is on potential energy, like how gravity causes things to accelerate through the potential energy of the arrangement - is lost that accounts for the creation of negative mass particles or whatever; conservation is observational, but we don't really know what 95% of the stuff being conserved is in the first place).
Hence it can be consistent with the conservation of mass and energy.
This is very new research without a deep check by other groups and without experimental support, so wait 5-10 years before getting too attached to this result. Anyway, there are weird somewhat similar things that are cannon https://en.wikipedia.org/wiki/Vacuum_expectation_value
The technical details and the experimental support are very very very important to distinguish between weird things that are true and weird things that are false.