Remember
Buran 20 years ago? It made 2 orbits in space, reentered & landed authomatically, and even corrected for wind shear. Why can't a capsule of modified AshMs reenter after separating from a BM? Shutes could be used on descent to slow it down if the speed is too high. At the right velocity, those missiles would eject and start their own powered flight.
I have not forgotten the Buran, but the Buran was a space shuttle/plane and therefore the re-entry flight would be quite different than that of a BM.
As for creating a capsule to deploy some form of ALCM, it might (repeat, MIGHT) be possible. To my knowledge, no one else has successfully done so. In point of fact, I am not aware of any project or program where someone has attempted to do so (any DefPro able to chime in here?).
There are a number of potential issues which I forsee causing problems, if such an engineering design were to be attempted. The first would be at what altitude, velocity and angle of approach would the ALCM be able to safely/reliably deploy on its own? All of this would effect the methods used to retard the ALCM to allow for launch. I would expect that the greater the kinetic energy of the inbound ALCM, and/or the higher the altitude needed for deployment, the larger something like a parachute would need to be. It might possibly be too larger for parachutes to be effective. IIRC for air-dropped lightweight torpedoes (as from ASW helicopters or MPA) those dropped from the P-3 Orion cannot be dropped from higher than 12k ft, otherwise the 'chute is unable to slow the descent of the torpedoe sufficiently. The case for an ALCM might be similar. Another issue would be to ensure that either the ALCM sensor code has the correct vector to detect the target, or having a sufficiently reliable datalink to guide the ALCM to the target, or to where it can detect the target on its own with onboard sensors. Otherwise a BM carrying an AShM/ALCM fired at a ship or target off the East Coast could end up with the ALCM heading west once it exits the inbound capsule...
Do not forget, in order to deliver something like the US AGM-84 Harpoon (air-launched version) the capsule would need to capable of carrying an object that is 500+ kg, and ~4m x .35m, in addition to whatever would be needed for allowing the ALCM to deploy.
The last issue is just how effective would such a system be, assuming everything worked correctly compared to other means? By effective I mean both in terms of successful strikes, as well as cost. IMO such a system would not effective in terms of cost per successful mission when compared to other methods of carrying out such a strike. Given the number of long ranged ALCM or AShM designs available, using a BM to deliver one would only make sense if one did not have a long-ranged ALCM, or if the range was such that an ALCM could not reach the target, even the long-ranged ones. For the first, I would expect that the engineering and manufacturing issues would be such that it would be less expensive to develop or by the rights to make a long-ranged ALCM. For the second, then one is likely talking about taking intercontinental BM shots. That, whether or not it would be successful, adds an entirely new element into the idea.
Assuming a country were to do so, then the US, Russia and likely France, the UK, Australia and possibly China & Japan would detect the ICBM being fired. Given the 'normal' warhead used in an ICBM, the countries with nuclear weaponry that detect such an attack would, for their own security, begin preparations to launch their own nuclear strikes as part of MAD. This in turns leads to the possibility of an accidental nuclear exchange because someone was taking a shot at some ship somewhere using a BM.
-Cheers