Rabbi David Tzvi Hoffman was a most unusual rabbi for his time. His attitudes toward a perspective convert was pretty liberal–especially when compared to the positions taken by numerous Modern Orthodox and Haredi rabbis living today. It is unfortunate the past generations of rabbinic scholarship expressed far more imagination and creativity than the newer generations of rabbinic leaders we have today.
R. Hoffman was born in Verbo, Hungary in 1843, and he died in Berlin in 1921. His great erudition encompassed all branches of Torah knowledge: Bible, Talmud, Midrash, and Halacha. He was the type of quintessential scholar who could critically discuss various theories concerning biblical criticism and the history of rabbinic thought while still remaining a loyal and devoted son to his sacred tradition. Rav Hoffman also served as rector of the Hildesheimer Rabbinical Seminary in Berlin, he educated generations of rabbis and communal leaders. His collection of responsa, Melammed Le- Ho’il, deals with a wide range of modern problems.
In this specific case, Rabbi Hoffman deals with a Jewish woman who marries a gentile man and later discovers she is pregnant by him. It is unclear whether the woman’s family exerted pressure on the gentile husband to convert; or alternatively, he chose to do so for the sake of his wife. Rather than sending the couple away, Rabbi Hoffman found a way to welcome the woman’s husband to the Jewish fold. He explains:
“The Code of Jewish Law states, ‘We refuse any convert who comes to be converted because he desires a certain Jewish woman. However, the school of Tosfot disputes this opinion in BT Yevamot 24b based on the well-known rabbinic story concerning the Gentile who appeared before Hillel and wished to convert so that he might become a High Priest. Obviously, the man had ulterior motives for converting. Nevertheless, Hillel still converted him. Another Talmudic story relates how a certain woman who came before Rabbi Hiyya and wanted to convert to Judaism so that she could marry a young Talmud scholar (BT Menachot 44a).
In both cases, Hillel and Rabbi Hiyya felt confident that these candidates would eventually become sincere in their motivation.  From this principle, rabbinic tradition teaches that the court has the right to make special waivers when it sees fit to do so. Ergo, it is permitted to accept him as a convert.
Now in the present case we are examining, here is a man who already married a Jewish woman and now she is pregnant. If a Beit Din refuses to accept him, he is determined to remain married to her whether it is a biblical prohibition or not!  If so, is it not far better that we accept him as a convert than that he should be married to her in sin? Now one might object and claim “How can we ask the Beit Din to countenance the sin of accepting a convert who is not converting for the ‘sake of Heaven’ in order to deliver this woman from a greater sin that will affect the rest of her life, for she was the one who originally sinned in the first place?”
To this we may reply: firstly, although she began in sin by giving herself to a Gentile, nevertheless she is like one who is helpless since she is now pregnant and cannot endure her shame unless she be married to him by Halacha, she is fearful that no man will have her for a wife and that she will remain forlorn for the rest of her life, she is like a person who is a victim of circumstances.
Moreover, if she remains married to this gentile man, her Jewish children may follow after their father and live a gentile life and will become sinners. And what sin have these innocent sheep committed that we should allow them to be alienated from their faith? This being the case, wouldn’t it better that the Beit Din should commit a “minor sin” of accepting this convert, so as to accustom him to living a Jewish life so that there will be sterling Jewish offspring from this Jewish couple.
Still and all, the court must warn the gentile to be careful in observing Jewish law, especially with regard to the Shabbat and forbidden foods. It would be apropos to receive a promise from him in lieu of a formal oath.” 
 Cf. R.Yosef Hayim’s Sefer Chukei Nashim (17).
 Minchat Yitzchak Vol 6 Responsa 106.
 Cf. the Responsa of Rav Moshe Schick in E.H. 37.
 Adapted from Melamad Liho’eel YD. II: Responsa 83.