When you leave the company can choose to buy back (essentially refund you for) unvested shares, in which case they take back the unvested shares. I imagine any company doing well will buy back the unvested shares.

If the company needs the cash more then maybe they'll let you keep the unvested shares, but since your usually-Common-Stock strike price is typically a lot less than what investors will pay for their Series-X shares it's likely they'd rather take back the Common Stock (?) even in cases of one or more transpired or likely down rounds (?).