In the special haftarah that is read for Shabbas Zachor, Sha'ul wages war against Amaleik and, in contradiction of his specific instructions from Shemuel HaNavi, he has pity on the king, Agag, and lets him live. Additionally, he does not heed the command to kill all the animals belonging to the Amaleikim and brings back those that were fit for sacrifice. Shemuel does his best to remedy the situation by personally disposing of Agag. Before smiting him with the sword, Shmuel declares poetically (Shemuel I 15:33) "As your sword has rendered women childless, so shall your mother be childless among women."
This statement may be understood merely as poetic irony. However, R' Chaim Kanievsky understands it literally and points out that we see from this statement that Agag's mother was still alive. Wasn't he the only Amalekite left alive? Agag's mother must have been from another nation. R' Chaim therefore concludes that a foreigner who marries an Amaleiki is not included in the commandment to wipe out Amaleik. However, in accordance with the guidelines of the gemara (Kiddushin 67) pertaining to the lineage of gentiles, her children are considered Amaleikim.
With this, R' Chaim explains another interesting twist in the story. According to the Ba'alei Tosafos on Parshas Beshalach, on that one night of captivity, Agag had relations with a donkey. This donkey was, in fact, a woman who made herself appear as a donkey through witchcraft. It was this propensity for witchcraft which demanded that even the animals had to be killed. This woman gave birth to a son from whom Haman descended. It is clear that this woman was among the Amaleikim. Why was she not killed? Only the animals fit for sacrifice – donkeys not included – were saved. Therefore, she must have been spared while still in the form of a human. Once again, the only justification for this could be that she was the wife of an Amaleiki who in fact hailed from another nation.