  The decays of exotic states discovered experimentally always proceed via the
strong and electromagnetic interactions. Recently, a tetraquark state with the
quark content $bc\bar{q}\bar{q}$ was predicted by Lattice QCD simulations. It
is below the mass threshold of $D\bar{B}$, which can only decay via the weak
interaction. In this work, based on the decay mechanism of $T_{cc}$ as a $DD^*$
molecule, we propose that the decays of the $bc\bar{q}\bar{q}$ tertaquark state
as a $D\bar{B}$ molecule proceed via the Cabibbo-favored weak decays of the
$\bar{B}$ or $D$ meson, accompanied by the tree-level decay modes and the
triangle decay modes. Our results indicate that the branching fraction of the
$D\bar{B}$ molecule decaying into $\pi^+ K^{-} \bar{B}^0$ is sizable, which is
a good channel to observe the $D\bar{B}$ molecule in future experiments.
