What is the Halacha in the following case: Reuven and Shimon are brothers. Reuven marries Rachel and has no children (Rachel is not pregnant). Shimon decides that he wants to be married to Rachel, and kills his brother to get his wife. The murder was with עדים והתראה (witnesses and prior warning). Is Shimon allowed to do yibum on Rachel before he is executed? Or would be exempt from doing Yibbum even if he does not end up getting death penalty because he actually killed her first husband ?
In the time when Bet Din executed people, there was no waiting around.
As soon as the witnesses were interrogated and the sinner found guilty, he was executed immediately.
So much so that Beth Din would kill an expectant mother if she was found guilty, and not wait for her to give birth.
So why would they wait for the murderer to do Yibum?!?!?!
Even if there was no warning or eidim, since a woman wouldn't want to marry a murderer, so she would not be forced into doing such a yibbum and the beis din would protect her from a murderer, so he would be forced to do halitza and let her free to marry someone else. If they killed him first like in your case where there is obviously noone to perform Yibbum.
The source of this is the Gemoro Yevamot 4a -
אמר רב ששת אמר ר' אלעזר משום רבי אלעזר בן עזריה מנין ליבמה שנפלה לפני מוכה שחין שאין חוסמין אותה שנאמר (דברים כה, ד) לא תחסום שור בדישו וסמיך ליה כי ישבו אחים יחדיו -
How do we know that a yevama that ends up being bound to levirate marriage in front of a leper that we don't muzzle up her protests (rather we force the man to do chalitza) as it says immediately after the parsha of yibbum "you shall not muzzle an ox during its threshing."
Rashi -אין [סותמין] טענותיה לכופה להתייבם לו אלא כופין אותו וחולץ-
we do not block her complaints to force her to do yibbum rather force him to do chalitza. All the rishonim agree as long as she has a legitimate claim she can force a chalitza although tosfos says if it is not desease related like מוכה שחין the beis din should promise money from her to the the yavam to do chalitza, then as soon as she does chalitza she doesn't have to pay anything as we pasken chalitza mutees kasheira - a mistaken chalitza is valid.
This is a quote from Beis Yosef even haezer165:
ורש"י כתב דלאו דוקא מוכה שחין אלא בכל אמתלאה שתתן לדבריה וכו' ור"ת פסק הלכה כסתם משנה דפ"ק דבכורות (יג.) ולפי פסק שלו אף בלא אמתלאה -Rashi writes any serious complaint we force him to do chalitza and Rabeinu tam writes even without a serious complaint we force him to do chalitza as we (ashkenazim) hold its better to do chalitza since we don't have right intentions so the beis din anyway force him to do chalitza.
Rambam is also quoted by Beis Yosef:בה' אישות פי"ד שכופין את הבעל לגרש את אשתו כשהיא מורדת ואומרת מאיס עלי וכ"ש יבמה שכופין את היבם לחלוץ -
we force the husband to give a get to the women when she says he is disgusting to me and how much more so a yevama we force him to do Chalitza on her since we do not say in such a case yibbum is better than chalitza.(sefardim hold yibbum is preferred over chalitza).
There is no link between the killing act and the zika. He can make chalitsa and Ybum. To mafkia zika there are arayot and asse plus lo taasse (and I think asse alone too) only. Following Rav Gidel in name of Rav (Yebamot 20a) there are lavim, in which the zika permitted and obligated chalitsa only (a weak zika), but the Rava makes a tyuvta against. The murder is not a case of arayot. He is a bad person, but this doesn't interfer with marriage rules.If there is a special din derabanan against the Ybum, I didn't see (this is not a proof, but the duty to furnish a proof is for the hypothetical chiddush that he is prohibited to make Ybum). To make him potur from chalitsa is not a possibility for a din derabanan.