@Mma ******
no. Your permission to stay ends your last day of work. There's no magical 7 days to leave. You also need to cancel your work permit with documentation from your company that states your last day of work. You can go about a week early and cancel it for the future. Then take the same documents and your cancelled work permit to the immigration office that issued your work extension and cancel that about a week ahead of time as well. If you don't do this you cannot apply for another long term extension in Thailand until you do, and you'll be fined 20,000 baht for failing to notify immigration about your change in status which you agreed to do when you signed the paper for your extension.
Once you cancel your work extension is when you would apply for your non-O visa. In the same visit to immigration even. But you need to check with them if they'll allow the change from work extension to non-O visa and if they will, what the requirements are.