First of all, in no way do I have advanced knowledge of particle physics, quantum mechanics, or any other necessary scientific concept for a full understanding of this question. Secondly, this is purely hypothetical; I am a writer looking to explore fictional concepts that are guided by science, not strictly within its realm.
Could there be something like the Higgs field which gives particles their energy in a similar way to how the Higgs boson gives particles their mass? What conditions would there need to be for the existence of this field? Could it exist without changing existing, fundamental laws? Keep in mind that, as it's fiction, new processes can exist to allow it. I understand that the Higgs boson does not literally give particles mass; i.e: there aren't Higgs bosons clustered around particles and making them massive.
I'm guessing there's something fundamentally wrong with this question (meaning my understanding of energy and mass) that makes it unanswerable or difficult to answer directly. If you can find a way around it, hats off to you! And thanks very much to anyone who answers at all. Again, I really have no idea what I'm talking about, so feel free to brush the question off as complete nonsense.