Hmmm, I would say that the Process object itself shouldn't be maintaining the paused state. The process doesn't care whether or not it's paused, it just cares whether or not its update method is called.
Rather the 'paused' status of the application is managed by some higher level state of the application. For example, taking a game-engine approach, you would generally have a GameState system.
Given two game states "Active" and "Paused", the active state calls the processes update method and the paused state doesn't. This can be extended to other process management styles also ofcourse.
I just don't think 'paused' is a state that belongs to the process itself and should be externally managed by the application.