  Binary neutron-star mergers will predominantly produce black-hole remnants of
mass $\sim 3-4\,M_{\odot}$, thus populating the putative \emph{low mass gap}
between neutron stars and stellar-mass black holes. If these low-mass black
holes are in dense astrophysical environments, mass segregation could lead to
"second-generation" compact binaries merging within a Hubble time. In this
paper, we investigate possible signatures of such low-mass compact binary
mergers in gravitational-wave observations. We show that this unique population
of objects, if present, will be uncovered by the third-generation
gravitational-wave detectors, such as Cosmic Explorer and Einstein Telescope.
Future joint measurements of chirp mass ${\cal M}$ and effective spin
$\chi_{\rm eff}$ could clarify the formation scenario of compact objects in the
low mass gap. As a case study, we show that the recent detection of GW190425
(along with GW170817) favors a double Gaussian mass model for neutron stars,
under the assumption that the primary in GW190425 is a black hole formed from a
previous binary neutron star merger.
