Photons can be created and destroyed freely, since they don't have charge or mass. Turn on a light, and you create many photons. Any body (made of atoms) not at absolute zero temperature will spontaneously emit photons.
They are consumed just as easily. Most any bit of bulk matter will absorb a photon in the electrons on the surface, transforming the energy into density vibration. No mystery; electrons (being charged) can do that. It's the opposite process of emitting via thermal vibration.
So where does it go...… think of the electromagnetic wave, not the quantization of it. Vibrations in E field make electrons slosh back and forth. Moving charged particles create electric field changes in turn, which cancel out the wave and prevent it from propagating farther. Where does an ocean wave go when it hits the beach? It stops propagating so the wave (a phenomenon not an instance of an object) ceases to be.
The idea of particles makes you envision a thing that exists as an object, and that is misleading and detracts from the concept. The particle-ness in this case is just part of the rules that states that some physical interaction takes or gives energy on an all-or-nothing basis. That's seen in cases where an electron changes orbitals including when that is part of a chemical process. Bulk pigments that can absorb any frequency (in a range) freely still take exactly one wave's worth of energy at a time in units of amplitude described by Planck's constant.
Vibration --— dynamics that can be started and stopped --— is the underlying creation and destruction. Creating or destroying fixed sized units only is manifest in the rules for doing so, and does not represent an object in the sense that's bothering you.
More generally you wonder how something can disappear. Well, why not? Some stuff is conserved and can only move around; other stuff has no restriction. For producing light, you need to supply energy and balance the "spin". Those are individual attributes, not specific particles, and that is how such rules are generally found. An electron can be created if you also create a positron at the same time, to balance the charge total: you aren't destroying something or moving things from somewhere else, you are creating more things.
The current best model for explaining all this is Quantum Field Theory, where everything is fields and dynamic disturbances of them, with particles being emergent from the rules. IOW, just like the above explanations with the photon.
Where does a song go when you stop singing? It's a dynamical process, not a fixed object. It goes away when that process stops.
