If I have a residence permit expiring on the 31st of January, I need to stay in china until Feb 3rd

My residence permit expires on the 31st of January, however the flights to go home (Germany) during the first week of February are significantly cheaper than those in the last week of January. I would like to extend my stay in China just a few days past the 31st so I can book a cheaper return flight home.

Does anyone know what I should do, and how much it would cost to do this. Any advice around this matter would be greatly helpful! Thank you for the help!