  Motivated by the recent evidence for $B^+\to K^+\bar{\nu} \nu$ decays at
Belle II, we point out that fully invisible $B_d$ and $B_s$ meson decays are
strongly constrained by LEP. A reinterpretation of an old inclusive ALEPH
search for $b$-hadron decays with large missing energy allows us to place the
limits $\mathrm{Br}(B_d \rightarrow \mathrm{invisible}) < 1.4\times10^{-4}$ and
$\mathrm{Br}(B_s \rightarrow \mathrm{invisible}) < 5.6\times10^{-4}$, both at
$90\%$ CL. The $B_d$ limit is only a factor of 6 looser than the world-leading
one provided by the BaBar collaboration, while the $B_s$ one is the first limit
in the literature on this decay mode. These results are relevant in the context
of new light states coupled to quarks and exemplify the power of a future
Tera-$Z$ factory at FCC-ee to look for $B$ meson decays containing missing
energy.
