A rocket engine by it's nature is a tough device. Many of them survive orbital entry and that's 30MJ/kg. With the absence of air, only real damaging factor on s

A rocket engine by it's nature is a tough device. Many of them survive orbital entry and that's 30MJ/kg. With the absence of air, only real damaging factor on some device which isn't supposed to function, is neutron flux. Let's suppose the engine was XLR105-5, as used on Atlas-D, the contemporary ICBM. It had a diameter of 3.05m and mass of 460kg. So we could expect at least some recognisable debris to remain out of a rocket engine that absorbed 460 * 3E7 joules of energy through it's (3.05/2)^2 * PI m2 external projection, or up to 1.9GJ/m2. A 400kt nuclear device is 1.7E15J, thus (emitting across 4PI steradian of space), this amount of flux is achieved at only 266m distance. So at 266m or so, at least something will remain of the engine, and at 1km, not just the engine will be pretty much intact (that would be damage from entering of the 1st, not upper stage - only damage 1st stage engines get from reentering, is from the ground impact or water damage if falling to the ocean), but even the stage itself will be only partially destroyed. It's highly unlikely the stage was closer than 1km to the warhead at the moment of detonation.