  Many black holes (BHs) detected by the Laser Interferometer
Gravitational-wave Observatory (LIGO) and the Virgo detectors are multiple
times more massive than those in X-ray binaries. One possibility is that some
BBHs merge within a few Schwarzschild radii of a supermassive black hole
(SMBH), such that the gravitational waves (GWs) are highly redshifted, causing
the mass inferred from GW signals to appear higher than the real mass. The
difficulty of this scenario lies in the delivery of BBH to such a small
distance to a SMBH. Here we revisit the theoretical models for the migration of
compact objects (COs) in the accretion discs of active galactic nuclei (AGNs).
We find that when the accretion rate is high so that the disc is best described
by the slim disc model, the COs in the disc could migrate to a radius close to
the innermost stable circular orbit (ISCO) and be trapped there for the
remaining lifetime of the AGN. The exact trapping radius coincides with the
transition region between the sub- and super-Keplerian rotation of the slim
disc. We call this region "the last migration trap" because inside it COs can
no longer be trapped for a long time. We pinpoint the parameter space which
could induce such a trap and we estimate that the last migration trap
contributes a few per cent of the LIGO/Virgo events. Our result implies that a
couple of BBHs discovered by LIGO/Virgo could have smaller intrinsic masses.
