Is it true that the fallen angels would die if they didn’t get energy by preying on us?

This is quite true. This, in a sense, is the fullest and most dire and extreme an example of the power each individual has to determine their fate, in the sense that humans can choose to die and make this so. The fallen spirits can do this as well. Even though they are not incarnated physically, but are in a perpetual spirit form, they can nonetheless perish, and to be without energy will in fact result in their demise. And the description is quite accurate that in turning away from the light they are rejecting the life force itself, and this is the fate of the disconnection from the higher realm. They do very much require energy and will prey on other beings of all kinds to have this. They can indeed persist indefinitely, as long as there is suitable prey to obtain the energy. This remains a chronic problem unless an answer is found to break this cycle. This is what the human enterprise is all about, to surmount this circumstance, not by escape, but by solving the problem. This is the reason for our frequent admonition to heal the perpetrator in order to heal the victim. This is what is needed now for humanity, to help solve the problem of the fallen angels, to remove this scourge through healing, not through their destruction, and this will pay great dividends for all the beings subject to their predation. It is the ultimate answer and is the quickest way to a solution that serves all, including the angelics themselves. They are far more in need of rescuing than you are, as they live very much on the edge and in a very direct and absolute sense. You are deciding their fate. Your ignorance of their existence and inability to deal with them, as a consequence, condemns them to being in this sorry state of affairs as fallen beings and meddlers needing to prey upon the living human for energy to exist, with all of the subsequent problems it causes their human hosts. There is a far better future for all in bringing love to bear to raise everyone up, so they can once again approach and embrace the light and return to their former state of harmony with Creator.