Can you actually resign from an LDS Church calling or position?
Most members might say no, but there is a historical precedent for a resignation taking place.
On Oct. 6, 1946, Joseph Fielding Smith (the less well-known leader with that name, that was not the president of the church), submitted his resignation as patriarch to the church.
Although some more contemporary sources state that he was "released," he did submit his resignation for the calling to the First Presidency.
The newer Church News Almanacs state he was released, but the older almanacs confirm his resignation.
So, there you have it, for whatever it may mean, at least one church member did resign from a major calling and his resignation was accepted.
(Eldred G. Smith, the seventh and last patriarch of the church, replaced Joseph Fielding Smith. Eldred was put on emeritus status eventually.)