Given any photon, there is a frame of reference where it has any energy you like. Arbitrarily high or low. There may be a wavelength so long and an energy so low that you cannot detect it. But it is still a photon.
If it has an arbitrarily low energy and momentum and it scatters off a particle at rest in your frame, it will not deflect the particle very much. But a particle running upstream into it will see it as Doppler shifted to a shorter wavelength. There is a particle speed that will give the photon an arbitrarily short wavelength and high energy.
A frame of reference where the photon has $0$ energy is one where it has $0$ frequency. That is, at any point the phase is unchanging. This means the frame of reference would have to travel as fast as the photon. Since the photon travels at the speed of light, this is impossible. There is no such frame of reference.
Another place where this is interesting is in a gravitational well. Time runs slower on the surface of a planet. An observer on the planet will see a photon as having a high frequency and a short wavelength.
If the photon travels upward, any observer it may encounter at the top of a tower will have a faster clock. That observer will measure the photon as having a lower frequency and longer wavelength.
For a black hole, this effect becomes extreme. The closer you get to the event horizon, the harder it is to maintain a frame of reference like a planetary surface. A photon emitted on such an extremely high gravity planet will be measured to have the same frequency it would on a lower gravity planet. However, an observer far from the planet will see time as running extremely slowly on the high gravity planet. He would see the photon as extremely red shifted if it climbed up to him.
At the event horizon, it is impossible to maintain a planet like reference frame. Time
would stop. Such a photon would be infinitely red shifted and have $0$ energy. It would also take an infinitely long time to arrive, traveling as it would through slow-time regions.
Inside the event horizon, all trajectories lead to the singularity at the center. The photon would never reach the event horizon.