While my understanding of quantum physics is better than the average high schooler, it is still very limited (I possess no mathematical understanding of the standard model whatsoever among many things). Hence, you can gauge the probability of the correctness of my answer. Considering this, here’s my answer:
We don’t know. We lack a lot of experimental data in quantum physics to answer this question.
First, we have never observed a massless electron. Hence, we have no idea about what would happen if we could do as you said.
Then, we have no experimentally proven theory of quantum gravity. We simply have no idea how gravity functions at the quantum level. Let’s say we make the rest mass of a massful particle zero by manipulating the Higgs field. What would happen to its gravitational mass? All of general relativity is based on the assumption that inertial mass = gravitational mass. This is called the principle of equivalence. However, we don’t know if this stays true at the quantum level. We don’t even know if the goddamn graviton exists or not.
While my understanding of quantum physics is better than the average high schooler, it is still very limited (I possess no mathematical understanding of the standard model whatsoever among many things). Hence, you can gauge the probability of the correctness of my answer. Considering this, here’s my answer:
We don’t know. We lack a lot of experimental data in quantum physics to answer this question.
So the answer is this: ¯\_(ツ)_/¯