Extension to Residence Permit

Applications for extensions to residence permits are submitted to the Finnish Immigration Service prior to the expiry of the existing residence permit. It is recommended to submit the application for extension well before the expiration date of your current residence permit. If your previous residence permit expires during the application process, you are allowed to stay in Finland but you are not allowed to work before you receive the new permit.

See http://www.migri.fi/extended_permit

Travelling during application process
If you come from a country that is not exempt from the visa requirement and have not been granted an extension to your residence permit, you cannot leave and return to Finland before the extension has been granted. If it is absolutely necessary to leave Finland, you need to apply for a visa at your nearest Embassy of Finland in order to return Finland.