Say for example in the case of x86-64 you have a program that makes use of avx-512 instructions or any other special purpose instruction, and the cpu in question does not support the instruction at the low level such as a haswell based cpu, how does this situation get resolved?
Is the program simply just not able to run (my first thought) or is there a way for the cpu to still run the program using the instructions it does support, however it will simply not receive the performance advantage offered by the instruction in question?
If the program checks CPU features and avoids actually run unsupported instructions, you just miss out on performance. Libraries like x264 and x265 do this, setting function pointers when they start to versions of functions that are the best supported version for this CPU.
If you do run an unsupported instruction (e.g. because you compiled with gcc -O3 -march=skylake-avx512 to tell the compiler it could assume AVX-512 support) there are 2 possibilities:
lzcnt decoding as bsr).