Dead liver tumor tissue Question

I have a friend and also my father who were recently dianosed with stage IVcolon cancer and liver mets.
Question is :
when the CEA numbers go down drastically it suggests some of the tumors in liver could be dead tissue even though CAT scan shows not much change (or at least thats my understanding...I heard PET scan is the only way to really see if the cancer is still alive).
Question: what happens to dead tumor tissue in liver? Does it need to be surgically removed? Do they just leave it there?

Is it more common for tumors to shrink during chemo or die and stay the same size?

Thanks,
Sue