I think so. Often with my obsessions they end when I 'split' and move from the idealization stage to the devaluation. If the person is around me, their 'flaws' are more accessible. It sounds horrible, but I can devalue the person a lot easier when they are accessible and thus end the fantasy/ obsession. Sure devaluing is unhealthy, but it is certainly convenient for getting rid of an obsession.

If the person is dead, well that is not the case --the circle of idealization will continue on. There are a few things we can do, but we have to be entirely ready to give up the obsession (this is hard, obsessions are soothing and fantasies are a pleasing break from reality, I know that my obsessions definitely bring me comfort why would I want to get rid of them?). But if we really do:

-we have to get rid of anything to do with the person/ thing (throw out books, posters, pictures or give them to a friend to hold onto if we can't part with them just yet). removing the 'stuff' from your space can help with closure.
-use mindfulness and distraction to redirect thoughts. When we feel a fantasy coming on think about something else that excites you: a concept in a movie, a story you read, a new hobby. Practice breathing and meditation...need a guide? go here: www.audiodharma.org. Sit quietly. when you feel your mind going back to the person, bring it back to your breath.
-sounds harsh, but go and flirt whether online or in person, realize that this person is not the only one.
-practice mindfulness all day everyday as often as you can: be aware of reality and the sensate. do things to stimulate your senses and bring you back to reality when your mind wanders off.
Just a few things you could try...

I can relate either way, I have obsessions and am not ready to let them go...

ps. B, I just want to thank you and say that I admire your honesty and bravery in this thread, it is not easy to talk about such deep feelings and thoughts. Thank you for inspiring us with your honesty.