One choice is to take the severance and leave. That is often the best choice. Fighting your kind of situation is very difficult and will take a very serious toll on you, both mentally, physically and financially.
There are exceptions. If you are, for example, over the age of 50 in Silicon Valley, your chances of getting a decent job are very low. In any case, you must evaluate your own situation based on where you live and work, your age, your skills, network, etc.
If you have few if any alternatives, the best choice is probably to fight. But it won't be easy. And there is no guarantee you will succeed.
To fight, you will need legal counsel that specializes in employment law. You MUST get your attorney to make what is called a "demand letter" to Cisco. This demand letter will describe what has happened to you, and ask for the PIP to be cancelled.
It is critical that this demand letter be sent to Cisco before the PIP starts. Your attorney, surprisingly, even if they are good, may not know this. Why? Most individuals go to an employment attorney after they have been terminated. So many lawyers have very little experience in a situation like yours, where a PIP has been threatened but has not actually started.
This is why legal action is needed so quickly. Why? Once the PIP starts, it far more likely you will be terminated. On other hand, if Cisco gets a demand letter from your attorney prior to the PIP starting, Cisco may reconsider the PIP and even take it off the table entirely.
So if you act, act quickly. Do not hesitate.
Unfortunately, even if you stop the PIP, your manager is likely to do everything he can to make your work life insufferable. There are many ways a manager can do this. They are likely to be either illegal or completely against Cisco written policies. But that doesn't matter. Cisco pretty much lets managers do whatever they want to do - even if their actions are illegal or against Cisco policies or both. Do not expect HR to protect you at all.
What is worst is that once you fight Cisco, you will be effectively placed on a black list and your chances of a transfer inside Cisco are extremely low. Of course, you are not on a PIP and should be allowed to transfer. Doesn't matter. You will be on a secret blacklist and a normal kind of transfer won't happen.
This means you will probably be stuck with your manager. And that manager is going to want to get revenge on you for fighting the PIP and bringing in legal counsel. Your manager will do everything possible to make you fail and make you miserable. Their thinking is simple: if they make you suffer long enough, you will either give up and leave, or they will make you fail, and then restart the PIP.
For this reason, it is critical in the demand letter to demand a transfer because of the toxic behavior of your manager. That is, you want not only to stop the PIP but get a transfer as well.
My advice to you, if you have other options, is to take the severance and leave. Fighting Cisco is not easy, either mentally, physically or financially. But if you do fight, get an attorney and act quickly before the PIP starts.