You are misreading the statement,
The photon may be absorbed
means that the particle is a composite one, so that the photon may raise the atom, for example, to a higher energy level, the photon absorbed completely.
or a new photon may be created
Means if the scattering is not elastic, part of the energy of the photon is transferred to the particle and a lower energy (new) photon leaves, as in Compton scattering , look at diagram b here.
It is true that photon number is not conserved, but each photon particle-vertex depresses the crossection by a factor of (1/137) at least, so extra photons are not very probable. If the electron acquires a lot of energy in the compton scatter it may interact with a field of an atom and give off a second photon, but that is not what the statement is about.