  In this paper, we prove that a sequence of weak almost K\"ahler-Ricci
solitons under further suitable conditions converge to a K\"ahler-Ricci soliton
with complex codimension of singularities at least 2 in the Gromov-Hausdorff
topology. As a corollary, we show that on a Fano manifold with the modified
K-energy bounded below, there exists a sequence of weak almost K\"ahler-Ricci
solitons which converge to a K\"ahler-Ricci soliton with complex codimension of
singularities at least 2 in the Gromov-Hausdorff topology.
