If a married man who is childless is executed by beis din, does his brother still have an obligation to perform yibum?
Bamidbar 27:3, quoting Tz'lofchad's daughters, who were seeking land in Israel:
אָבִינוּ מֵת בַּמִּדְבָּר וְהוּא לֹא הָיָה בְּתוֹךְ הָעֵדָה הַנּוֹעָדִים עַל ה׳ בַּעֲדַת קֹרַח כִּי בְחֶטְאוֹ מֵת…
Our father died in the desert; he was not among the group who met against God in the group of Korach, but died for his own sin…
The Sifre (ad loc.) comments:
והוא לא היה בתוך העדה זו עדת מלינים הנועדים על ה׳ זו עדת מרגלים בעדת קרח זו עדה של קרח כי בחטאו מת שלא החטיא את אחרים עמו
"He was not among the group", the group of complainers; "who met against God", the group of spies; "in the group of Korach", the group of Korach; "but died for his own sin", that he did not cause anyone else to sin with him.
Malbim on the Sifre:
היל״ל והוא לא היה בעדת קרח וע״כ הוציאו מאריכות הלשון שכללו כל הנועדים לחלוק על ה׳ כמו מתלוננים ומרגלים ועדת קרח ביחוד שכולם לא נטלו חלק בארץ… וגם י״ל מפני שעקר טענתם היתה מכח יבום ועדת קרח ואינך אין להם חלק לעוה״ב ולא שייך אצלם יבום לתקן נפש המת לז״א שהוא לא היה מכללם כי בחטאו מת ולא החטיא אחרים ומיתתו כפרה וי״ל חלק בארץ וחלק לעוה״ב
The pasuk should have merely said "he was not in Korach's group"; from the extended description, the Sifre derived that the daughters of Tz'lofchad included all those who met to differ with Hashem, like the complainers and the spies and Korach's group in particular, as all these had no portion of land in Israel…. One can also say that [they mentioned these groups] because their main claim was a yibum-type claim. Korach's group and the others had no share in the world to come, so yibum has no bearing on them, as it does not fix their souls. So the daughters said that their father had not been in these groups — he died for his own sin, without causing others to sin — so his death is an atonement [for him] and he has a share in the land and in the world to come.
The Malbim is saying that Tz'lofchad's daughters' claim was a yibum-type claim. While I don't know what he means by that, he definitely seems to be implying that anyone with a portion in the world to come could have yibum-type claims apply to them after death. Most of those killed by bes din fall into this category, and yibum would seemingly then apply.