If the request is rejected by person 2, then the process should return control (i.e. a new task) to person 1. Therefore if no tasks exist for a process we can assume the process is complete and approved.
If an explicit notification is required, you can use an email, SMS or other notification mechanism should suffice.
In reality, having tasks disappear is actually good BPM practice. If we need to keep track of completed tasks, we should create records in a system of record database, although one would question the value of such a record (unless reporting on the number of approved/rejected requests is required).