No, you DO NOT work as soon as you are notified. You don't even do a handover or KT.
You are no longer employed by Cisco after and LR.
In my experience w/ the 2011 and 2016 major LRs, some impacted employees were expected to do handover's and or KT. For my team in 08, the impacted people were expected to email the manager a "brief" status of what they were working on, what needed to be done, and then they were expected to be "invisible". They could use the office fax machines and printers, Internet, etc. but were encouraged to work from different buildings or come in after hours so as to not be around those who were not impacted. For the different team I was on in 16, the manager basically said to make sure that our "documentation" was current on the wiki, and if we were willing, they could have a working lunch w/ the person who was taking over their responsibilities to do KT and the manager would expense the lunch. IIRC, it was a nice $15-20 lunch instead of cheap, fast food.
But, yes, you're not expected to work once you're notified. Unlike what @1ojz+1nFXoWdO said, you are an employee for that first 30-ish days while you deal with transferring your Cisco mobile # to a self-paid plan if you had a Cisco phone, get all the details of your 401(k) and ESPP/RSUs, etc. and start turning in your Cisco corporate card, keys, etc. During that last 30 days, you can try to find another internal role, but few manage to make that transition. Then you turn in your badge and laptop on your last day and you're done.