I'm trying to predict the survival curves for customers, knowing that for some rare customers after a certain time the survival probability has a jump. As far as I understand Cox Proportional Hazard and Accelerated Failure Models, they, in in layman's terms, take the average survival over time of the whole population and than multiply that with a constant, which is dependent on covariates. As those jumps are really rare and happen at different points of the lifetime, the average survival curves don't have any jumps in my case. With multiplying those curves with a constant, I can't model those jumps. Have I understood that correctly? If so, is there a way to predict remaining survival, knowing, that the survival probability will make a jump at a certain time?

I'm trying to predict the survival curves for customers, knowing that for some rare customers after a certain time the survival probability has a jump. Those jumps are due to endings of minimum contract duration. E.g., some customer commit to stay for 6 month. We know that those customers (usually) stay for 6 month. After that they can cancel there subscription on a monthly basis (thanks @EdM for the advice to include that information in my question). As far as I understand Cox Proportional Hazard and Accelerated Failure Models, they, in in layman's terms, take the average survival over time of the whole population and than multiply that with a constant, which is dependent on covariates. As those jumps are really rare and happen at different points of the lifetime, the average survival curves don't have any jumps in my case. With multiplying those curves with a constant, I can't model those jumps. Have I understood that correctly? If so, is there a way to predict remaining survival, knowing, that the survival probability will make a jump at a certain time?