It would seem plausible that without presenting a residency card you'd get dinged for overstaying back to whatever date immigration determines to be your last entry date.
If you do show your residency card, and it is expired, as WW says it may be confiscated and you will likely have to pay anyways. Not having an old card to turn in with your renewal application kicks your application into the "special circumstances" pile and we all know how much functionaries here like special circumstances. It would be nice if the fees were calculated from the date of expiry but that's not likely.
Paying the $10 to come back I don't think would be a deal breaker for anyone and is much less painful than getting a police report to account for not having a residency card to turn it with the renewal.