Examples I've seen were the Ottomon Empire's elite foot soldiers, the Janissaries, as well as administrative positions such as the Chief Eunuch, a man who (at one time at least) controlled an impressive network of inter-governmental spies through which he could gain leverage over generals and political figures alike. How did this come to be? And with military and governmental leverage did they ever attempt anything like a coup?
The Janissaries were not eunuchs. As in other courts around the world, the sultans kept eunuchs in high ranking household positions because they were in contact with the sultan's wives and concubines, and as eunuchs posed no threat to the harem. But eunuchs weren't a particularly large part of Ottoman society.
Do you mean slaves generally? Because how foreign slaves came to absolutely dominate Ottoman politics, and the politics of virtually every Islamic state for almost a millenium is a different story, and a good one. Slave soldiers, and former slaves launched coups and counter coups almost constantly and were basically the defining feature of Ottoman political life.