I imagine that until you cancel the privacy with the company that it will remain regardless, and of course keep rebilling you, they will hope that you will forget too
And may I ask what registrar will let an expired domain name keep its WHOIS privacy service? The surefire answer to the OP's question is to read the registrar's agreement, or to ask the registrar directly.
Ah, once it is expired, the whois info typically reverts to the registrar, or NOTHING... It' just expired... at that point, no one is attached to the domain, therefore there is no information to see or not see.
There are whois history services that keep track of these, such as: http://domain-history.domaintools.com/?q=mywebsite.com&page=results (i guess you need to be a paid member to monitor those though) So thru such services people may still contact you, if that's what you wonder, or if it's you trying to contact the previous owner of a domain.