In an atomic environment, a $\beta$-decay process competing with positron emission is electron capture, in which the nucleus absorbs one of its cloud of atomic electrons, emitting only a neutrino.
$$p+e^-\rightarrow n+\nu_e$$ Such a process often called K-capture since $e^-$most likely to come from the innermost K-shell of atomic electrons.
An outer electron replaces the "missing" electron. An x-ray, equal in energy to the difference between the two electron shells, is emitted. See the following.
Now as the outer orbital electron takes place the misplaced one, Isn't another position is vacant? Then What would happen? Is the upper once again take the place of the lower site? Then Does this process repeat again and again? Does that imply there would be many x-ray emissions?