Hey Marc,
This technique is possible to do, and frequently used by game developers, and is called savegame file. Main question here is: what information we need to startup process from prevoius state? For a game you do not have to dump all registers, dump whole memory, often you cannot do that due to insufficient access privileges. Saving state of all necessary objects in the game is good enough.
Achilles, just think what data is necessary to invoke your proccess from previous state, and load it from file on startup. When process exits, save all necessary data to file, or registry, or whatever storage area you wish.

thats my opinion
Hob