I don't have any experience with reporting a lost passport to the Police, but are you sure they are going to care that you are out of status? Perhaps someone else can enlighten you on the process and what questions they ask at the police station but if you don't have your passport, then how are they going to know your visa expired? I doubt the local police station is going to concern themselves with deporting you, if anything you might be referred to CIC and they may give you a certain amount of time to leave on your own terms before deportation (because why would they use tax-payer funds to pay for your flight when they can make your own arrangements).
I guess it depends on how out of status you are and what you have done about it. If your visa expired more than six months ago and you have not bothered to resolve the situation with CIC, then I guess it is a case of lying in the bed that you have made for yourself.
