  We study the semileptonic $B_s$ and $B$ decays into the $D_{s 0}^{\ast}
(2317)$ and $D_{0}^{\ast} (2400)$ resonances, respectively. With the help of a
chiral unitarity model in coupled channels we compute the ratio of the decay
widths of both processes. Using current values of the width for the
$\bar{B}^{0} \to D_{0}^{\ast} (2400)^{+} \bar{\nu}_{l} l^{-}$ decay we make
predictions for the rate of the $\bar{B}_{s}^{0} \to D_{s0}^{\ast} (2317)^{+}
\bar{\nu}_{l} l^{-}$ decay.
