I pointed out in response that the Biblical text itself also does not claim that Vashti was executed. That is, rather, a Rashi:
that Vashti did not come: and therefore, she was executed.The pasuk itself merely states:
|ט אִם-עַל-הַמֶּלֶךְ טוֹב, יֵצֵא דְבַר-מַלְכוּת מִלְּפָנָיו, וְיִכָּתֵב בְּדָתֵי פָרַס-וּמָדַי, וְלֹא יַעֲבוֹר: אֲשֶׁר לֹא-תָבוֹא וַשְׁתִּי, לִפְנֵי הַמֶּלֶךְ אֲחַשְׁוֵרוֹשׁ, וּמַלְכוּתָהּ יִתֵּן הַמֶּלֶךְ, לִרְעוּתָהּ הַטּוֹבָה מִמֶּנָּה.||19 If it please the king, let there go forth a royal commandment from him, and let it be written among the laws of the Persians and the Medes, that it be not altered, that Vashti come no more before king Ahasuerus, and that the king give her royal estate unto another that is better than she.|
That is, the decree, that shall not be altered, is that Vashti should no more come before the king, and that her estate/position be given to someone better than she. And she could not be restored to her position, because the law may not be altered, a plot point that comes up again later in the megillah.
It then seems that this pasuk is often interpreted in another way. Despite the imperfect tense of tavo, it is read as: "because she did not show before the king Achashverosh, her royal estate should be given to another who is better than she." The vav is then not "and" but introduces the consequence, and asher is because. And it fits nicely into Vashti's offense. (The translation above, in Rashi, of the dibbur hamatchil in Judaica Press seems to match this; although it is interpretable another way, that the way in which she would never come before him is by being executed.) Then, the punishment and her disappearance from the scene are left relatively unspecified, and one can interpret into this an execution.
Some people were surprised at my alternate reading, in which not showing up before Achashverosh was part of the punishment, but when considering it, liked it as a strong possibility.
(I see now that an early French exegete, I think Rav Yosef Kara (page 5), said like me, and added further that of course she was not executed, for if so, why would they need to write any law in the lawbooks of Paras and Maday?!)