Good question..
Daniel, who was a captive by King Nebuchadnezzar of Babylon when he conquered Judah, was very likely one of these men and First century historian Josephus asserts that he AND his three friends were these type of people:
"But now Nebuchadnezzar, King of Babylon, took some of the most noble of the Jews that were children, and the kinsmen of Zedekiah their king, such as were remarkable for the beauty of their bodies, and the comeliness of their countenances, and delivered them into the hands of tutors, and to the improvement to be made by them. He also made some of them to be EUNUCHS . . . Now among these there were four of the family of Zedekiah, of most excellent dispositions, one of whom was called Daniel, another was called Ananias, another Misael, and the fourth Azarias; and the King of Babylon changed their names, and commanded that they should make use of other names.
Daniel he (the King) called Baltasar; Ananias, Shadrach; Misael, Meshach; and Azarias, Abednego. These the King had in esteem, and continued to love, because of the very excellent temper they were of, and because of their application to learning, and the progress they had made in wisdom." (Josephus, Antiquities of the Jews, Book 10, Chapter 10, first paragraph)
Of course, with that considered, it's interesting how his being a eunuch adds a lot to his own struggle as a captive in Babylon. In regards to Daniel's emasculation is Deut 23:1 which states that one who is a eunuch may not enter into the congregation of the Lord....and if Daniel had been emasculated (seeing the depth of love he had for God painted throughout the scripture), it would have been something that he would have agonized over, and I think that something of that much importance to him would have found its way into scripture.
And we already have the possibility of others already BEING eunuchs before coming to Babylon. Before the Babylonians made others into eunuchs, the royal houses of Israel and Judah had a few eunuchs of their own. Two or three of these eunuchs threw the queen-mother Jezebel to her death at the bidding of Jehu (2 Kings 9:32-33). It is only natural that the queen would be attended by eunuchs. Another palace eunuch, Ebed-Melek, fished Jeremiah out of the cistern where the king imprisoned him, because Ebed-Melek feared for the prophets life (Jer 38:7-13).
In the third year of the riegn of Jehoiakim king of Judah, Nebuchadnezzar king of Babylon came to Jerusalem and besieged it. ANd the Lord gave Jehoiakim king of Judah into his hand... Then the king commanded Ashpenaz, the chief eunuch, to bring some of the people of Israel, both of the royal family and of the nobility, youths without blemish, handsome and skilful iin all wisdom, endowned with knowledge, understanding learngin, and competent to serve in the kings palan and to teach the the letters and langaue of the Chaldeans. Among these were Daniel, Hananiah, Mishael, and Azariah of the tribe of Judah. (Dan 1:1-6)
Being a eunuch had a lot of differing dynamics to it. Eunuchs were often in charge of harems; responsible for the protection and care of the wives of the king because they posed no threat sexually - and they were overseers of the beauty treatments for the women to make them presentable to the king (Esther 2:3, 12-13). The Ethiopian Eunuch was the treasure keeper (Acts 8:27) for Queen Candace and often Eunuchs were recognized for their spiritual sensitivity and wisdom and were chosen to advise the king. Because Isaiah prophesied that Hezekiahs children would become eunuchs in the palace of the king of Babylon (2 Kings 20:16-18), it seems logical that this was fulfilled when Daniel and the three Hebrew children (Shadrach, Meshach and Abednego) who were described as beautiful men (Daniel 1:4) - in addition to the fact that royal protocol in those days tended to have administrators made into eunuchs in order to protect the king's wife.
But God still had a plan for them. Isaiah 56 speaks of eunuchs (in regards to Deut 23:1) and foreigners in Judah who find themselves outsiders to the covenant, and the prophet assures eunuch and foreigner alike that there remains a place for them within the kingdom and within the worship of the one God of Israel. The implication was that eunuch and foreigner alike were treated as outsiders to the covenant - as if they had no secure place among Gods people, a situation which the prophet was proclaiming defunct. For even as they became part of someone elses empire, the prophets of Judah made sure the people understood that their God was trans-national...and beginning with the strangers and eunuchs in their midst, the covenant was extended to cover all outsiders.