I've done some math, and I think it should be possible. You'd need a very large, saboted flechette type projectile. 12 ga. should work. About 2" long, .451" diameter, and 800 grains should do. At 200 fps, it would penetrate about 15" in gelatin (including velocity loss due to going through skin first). I don't have any equations for drywall, but it would penetrate a total of only 1.3" of wood according to my models. Assuming they're the same, it would go through two layers of drywall, and just barely fart out the other side.
Unfortunately, 200 fps is low enough that heavy clothing plus skin would lower gelatin penetration down to 8.3". Raising the velocity to 230 fps would be sufficient to defeat most heavy clothing and still penetrate 12" (and would be very ironic), but that would also increase wood penetration to a hair under 3", so it would stop in the third wall. It would still be capable of inflicting a lethal, or at least very painful, injury after the first wall (approx 2-4" penetration), but would merely leave a bad bruise after the second one.
If the slug were made out of dead soft lead which wouldn't mushroom significantly on hitting clothing or flesh, but would flatten somewhat on hitting drywall, that may work best. If at 230 fps it flattens out to 1.5X the original diameter on impact with the wall, that takes the wood penetration back down to 1.2". Would be able to mushroom to .59" and still go 12" in a naked person, or .49" to go 12" after heavy clothing and skin.
Just as a comparison, 124 gr standard pressure 9mm will penetrate about 11.1" wood, and 230 gr .45 will go through 8.7".