[en] Doped band insulators, HfNCl, WO₃, diamond, Bi₂Se₃, BiS₂ families, STO/LAO interface, gate doped SrTiO₃, MoS₂ and so on are unusual superconductors. With an aim to build a general theory for superconductivity in doped band insulators, we focus on the BiS₂ family which was discovered by Mizuguchi et al in 2012. While maximum Tc is only ∼11 K in ${\mathrm{L}\mathrm{a}\mathrm{O}}_{1-<!--\; ???\; -->\mathrm{x}}{\mathrm{F}}_{\mathrm{x}}{\mathrm{B}\mathrm{i}\mathrm{S}}_2$, a number of experimental results are puzzling and anomalous in the sense that they resemble high T _c and unconventional superconductors. Using a two orbital model of Usui, Suzuki and Kuroki, we show that the uniform low density free Fermi sea in ${\mathrm{L}\mathrm{a}\mathrm{O}}_{0,5}{\mathrm{F}}_{0.5}{\mathrm{B}\mathrm{i}\mathrm{S}}_2$ is unstable towards formation of the next nearest neighborBi-S-Bi diagonal valence bond (charged −2e Cooper pair) and their Wigner crystallization. Instability to this novel state of matter is caused by unscreened nearest neighbor coulomb repulsions (V ∼ 1 eV) and a hopping pattern with sulfur mediated diagonal next nearest neighbor Bi-S-Bi hopping t’ ∼ 0.88 eV, as well as larger than nearest neighbor Bi-Bi hopping, t ∼ 0.16 eV. Wigner crystals of Cooper pairs quantum melt for doping around x = 0.5 and stabilize certain resonating valence bond states and superconductivity. We study a few variational RVB states and suggest that BiS₂ family members are latent high Tc superconductors, but challenged by competing orders and the fragile nature of many body states sustained by unscreened Coulomb forces. One of our superconducting states has d_XY symmetry and a gap. We also predict a 2d Bose metal or vortex liquid normal state, as charged −2e valence bonds survive in the normal state. (paper)