A process (parent) can execute another process (child). When a parent process is killed all the child processes are automatically assigned to the main system process called init. The init process is the first process that is started on your computer and is numbered as 1. If this process is killed the system will shutdown.
To see the tree of processes, you can use the command
A user can kill only the processes that the user has created not the processes of other users. Only root can kill the processes of other users.