Say the wavelength of a photon became so large that it approached the size of the observational universe. Does something unexpected happen?
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Theoretically there is no upper limit on the wavelength of a photon.
Since the whole universe is probably infinite, the observable universe is just a little part of it.
So when the photon's wavelength reaches the size of the observable universe, nothing unexpected happens, it can still keep growing.
Though, I would like to mention that the universe is expanding at an accelerating rate, and if the rate of acceleration reaches and surpasses the speed of light, then even the observable part of the universe could be expanding at a rate of higher then the speed of light. It is not clear how you would create this photon with this large of a wavelength. The wavelength of the photon in this case will not be able to reach the size of this observable universe. By the time you create the photon, the observable universe will have expanded at a rate higher then the speed of light.
It would require more than a Hubble time to emit such a photon so it does not exist yet.