Changing stop button behaviour

I want to achieve the following:

When the stop button of a running model is pressed, Simulink should not immediately stop the simulation. Instead the value of a constant block should be changed to 1, which in turn will trigger some behavior in the model (incl. triggering a stop block in the end).

• Is there a way to redefine the callback of the stop button in a Simulink window?
• Is there a way to use the StopFcn callback for this, i.e. setting the constant block and forcing the simulation to continue?