The 68000 series provided a trap (interrupt) for illegal instructions (i.e. the decoder did not recognise it) and was quite commonly used to provide customised instructions. The trap, IIRC, actually passed the offending instruction to the handler so it was possible to implement numerous interesting instructions in software.
This was not only possible, but positively marketed by (then) Motorola SPS (since rebranded to Freeescale and thence NXP).
This was,of course, not used in that many instances compared to all possible implementations using 68k series parts, but I have seen a single illegal instruction used to make a multiple instruction sequence atomic on the 68k series.