There are often calls for one portion of a state to secede and form their own state. For example, the recent Scottish referendum on seceding from the UK. But suppose it went the other way around, and England, Wales, and N. Ireland decided they didn't want to be unified with Scotland any more. But has there ever been a case where a state has unilaterally ejected a portion of itself? Are there any legal structures to handle such a situation?
Yes, there have been. Singapore is one prominent example.
The history of the Republic of Singapore began when Singapore gained its independence and became a republic following an ejection from Malaysia on 9 August 1965. (Wikipedia)
The merger in 1963 led to numerous economical and political difficulties and also racial tensions amongst Malay and Chinese communities, so the Malaysian PM voluntarily decided to expel Singapore from the united state.
Maybe this counts. Some of the former republics of the USSR did not want the dissolution of the USSR. In the most of the republics the 1991 referendum of whether to preserve the USSR gave results in support of the USSR preservation, additionally the leadership in some of the republics(Kazakhstan and Central Asia) did not want the dissolution either.
The dissolution was mostly pushed forward by the leadership of Russia, Belorussia and Ukraine, who concluded the agreement without participation of other republics.
While not an exact match, the example of Puerto Rico may satisfy a general idea of what you are looking for. Puerto Rico became a colony of the United States in 1898. Unlike the other colonies- the Phillipines and Cuba, Puerto Rico has never voted for independence. While there has been an independence movement there (one guy killed Truman's bodyguard, another planted a bomb in the U.S. Capitol), every time it has come to a referendum, the colony refuses to leave. Indeed, recently it even voted to become a state.
The problem is that the mainland United States Congress, which gets to decide the matter, however, has not acted on the petition. The argument will probably be made that Puerto Rico wasn't in the union - but the mainland refusing to let it join may hit the spirit of the question. if not the letter.
In general, absorbing Puerto Rico as a state would probably be a net loss to the federal government, but Puerto Rico knows it has much to gain in the deal. There have been attempts in the COngress and on the mainland to get Puerto Rico to go its own way, but it stubbornly wont.