The only reason a very small % of PIPed employees may be saved will to be show on paper that it was not a lay-off to avoid any legal battles. It may not have to do anything with the actual performance improvement so stop fooling yourself.
Accept the fact that passing of PIP will be a lottery just so corporation doesn't have legal liabilities, ...but what a lottery! — it is a curse to continue in the same rotten pond until someone finds a reason to get rid of you.