  Soft functions defined in terms of matrix elements of soft fields dressed by
Wilson lines are central components of factorization theorems for cross
sections and decay rates in collider and heavy-quark physics. While in many
cases the relevant soft functions are defined in terms of gluon operators, at
subleading order in power counting soft functions containing quark fields
appear. We present a detailed discussion of the properties of the soft-quark
soft function consisting of a quark propagator dressed by two finite-length
Wilson lines connecting at one point. This function enters in the factorization
theorem for the Higgs-boson decay amplitude of the $h\to\gamma\gamma$ process
mediated by light-quark loops. We perform the renormalization of this soft
function at one-loop order, derive its two-loop anomalous dimension and discuss
solutions to its renormalization-group evolution equation in momentum space, in
Laplace space and in the "diagonal space", where the evolution is strictly
multiplicative.
