From the moment when your contract ends you are considered unemployed and are legally allowed to stay in CH (up until the permit expires, anyway). During this period you can also apply for unemployment aid.

If you find a new employer, then you need to apply for a work permit again. As it says on the back of the paper that you've scanned, any change of employer requires a new application for a new authorization. The employer must apply for your permit, and the authorities shall process again your request (and therefore grant/deny it).

If you reach your permit expires' date as unemployed, in good faith (meaning that you actively tried to get jobs but no opportunity appeared), you have a lot of potential for getting the permit renewed since you paid for unemployment assurance and it's in your right to continue to receive it until you manage to get a new job (in CH or abroad by leaving the country).