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The Milky Way's satellite galaxies ("surviving dwarfs") have been studied fordecades as unique probes of chemical evolution in the low-mass regime. Here weextend such studies to the "disrupted dwarfs", whose debris constitutes thestellar halo. We present abundances ([Fe/H], [$\alpha$/Fe]) and stellar massesfor nine disrupted dwarfs with $M_{\star}\approx10^{6}-10^{9}M_{\odot}$ fromthe H3 Survey (Sagittarius, $Gaia$-Sausage-Enceladus, Helmi Streams, Sequoia,Wukong/LMS-1, Cetus, Thamnos, I'itoi, Orphan/Chenab). The surviving anddisrupted dwarfs are chemically distinct: at fixed mass, the disrupted dwarfsare systematically metal-poor and $\alpha$-enhanced. The disrupted dwarfsdefine a mass-metallicity relation (MZR) with a similar slope as the $z=0$ MZRfollowed by the surviving dwarfs, but offset to lower metallicities by$\Delta$[Fe/H]$\approx0.3-0.4$ dex. Dwarfs with larger offsets from the $z=0$MZR are more $\alpha$-enhanced. In simulations as well as observations,galaxies with higher $\Delta$[Fe/H] formed at higher redshifts -- exploitingthis, we infer the disrupted dwarfs have typical star-formation truncationredshifts of $z_{\rm{trunc}}{\sim}1-2$. We compare the chemically inferred$z_{\rm{trunc}}$ with dynamically inferred accretion redshifts and find almostall dwarfs are quenched only after accretion. The differences between disruptedand surviving dwarfs are likely because the disrupted dwarfs assembled theirmass rapidly, at higher redshifts, and within denser dark matter halos thatformed closer to the Galaxy. Our results place novel archaeological constraintson low-mass galaxies inaccessible to direct high-$z$ studies: (i) the redshiftevolution of the MZR along parallel tracks but offset to lower metallicitiesextends to $M_{\star}\approx10^{6}-10^{9}M_{\odot}$; (ii) galaxies at$z\approx2-3$ are $\alpha$-enhanced with [$\alpha$/Fe]$\approx0.4$.

Live Fast, Die $\alpha$-Enhanced: The Mass-Metallicity-$\alpha$ Relation of the Milky Way's Disrupted Dwarf Galaxies