Earlier quoted context omitted.
There are no circumstances in which it will turn around Note that you used the passive voice, as though the circumstances are completely out of the employee's control.
They are. Why anyone is willing to adopt the delusion that a "personal improvement plan" is about improving anything I cannot understand. The circumstances are far less severe and consequential, but I can only compare it to a political dissident in a totalitarian state being tortured so long that he eventually believes he was undermining some righteous, just society with his actions. You shouldn't take it as a person…
I've been a manager with HR in these kinds of conversations. At the point that we decide to put an employee on a PIP, it's because continuation of the current performance is unacceptable - not that the particular employe "must go", just the current behavior. We typically have lots of other employees performing at a higher level or with better attitudes, so it isn't just some random whim where we have it in for someone and are unwilling to allow for them to rectify the problem.
If the employee were to improve his or her performance (typically improve his or her attitude), as an employer we would be more than happy to continue that person's employment.
It's a defeatist attitude that becomes a self-fulfilling prophecy.