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1.
The opposite of engaged:

Outgagement (noun)- The state one enters after recently ending a relationship.

Outgaged (Adj./ Tr.vrb)- to be in a state of outgagement.
"Well, after fighting constantly for the last six months, Sara and I decided to get an outgagement."

"Man, I've had so much time since being outgaged."
by jobopants May 15, 2009