I feel that closing a relationship that was once open makes a huge change in both how things are run and the interaction between the partners. They no longer are allowed to look, they cannot have intimate relationships with others, and they cannot play in any way, shape, or form with people aside from the main partner.
For me, being monogamous, I do not experience any loneliness once a relationship is closed. It feels more relaxing, actually. But I do not know if that really answers your question. I've been starting any relationship that I've had lately as open until further notice, so when they have closed, it's felt better for me since I am monogamous. I cannot really say the same for the people I was with, however.