The modern term for this phenomenon is "spall", and yes, many modern vehicles are equipped with so-called "spall liners". These are basically a working equivalent to your rubber layer
IIRC, it's usually some kind of Kevlar matting that's attached to the inside of the vehicle armor in order to catch any spall (splash) that occurs due to hits on the outside.
I don't think you can treat the armor itself to prevent spall; remember that in the 1960s, the wonder anti-tank round in some countries was one that was designed
to cause huge amounts of spall ? HESH (or HEP if you're American) rounds basically work by detonating the round on the outside of the armor so that a large chunk comes off on the inside. (This was countered by installing spaced and composite armors on tanks, BTW.)