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We propose to search for the open heavy-flavor exotic states with the quarkcomponents of $Qs\bar u\bar d$ with $Q=b,c$ via their weak decays. If thereexist such exotic states below the $BK$ or $DK$ thresholds, they can only decayweakly. The advantages include: (i) the experimental backgrounds from thesecondary decay vertex are much lower due to the long lifetimes, (ii) theproductions are large enough for only one heavy quark in such states, (iii) thethresholds of $BK$ or $DK$ are about 260 MeV higher compared to the $B_s\pi$ or$D_s\pi$ thresholds of the configurations of $Qu\bar s\bar d$ or $Qd\bar s\baru$ , with a higher possibility to exist such weakly-decay particles, and (iv)if observed, their inner structures are easier understood since they can not beinduced by the kinematic effects.

Weak-decay searches for $Qs\bar u\bar d$ tetraquarks