  We examine the effect that the subtraction of multiple photons has on the
statistical characteristics of a light field. In particular, we are interested
in the question whether an initial state transforms into a lasing state,
i.e.,~a (phase diffused) coherent state, after infinitely many photon
subtractions. This question is discussed in terms of the Glauber
P-representation $P(\alpha)$, the photon number distribution $P[n]$, and the
experimentally relevant autocorrelation functions $g^{(m)}$. We show that a
thermal state does not converge to a lasing state, although all of its
autocorrelation functions at zero delay time converge to one. This
contradiction is resolved by the analysis of the involved limits, and a general
criterion for an initial state to reach at least such a pseudo-lasing state
($g^{(m)}\to 1$) is derived, revealing that they can be generated from a large
class of initial states.
