If a child who did not reach puberty and accidentally kills someone do they have to do the unintentional murder expiation.
Yes, according to the Malikis, Shafi'is and Hanbalis because they consider Kaffarah (i.e. freeing a slave) a right in wealth so it is analogous to other financial rights in property, so the guardian of the child's property must carry it out. In case of inability to free a slave the guardian can not observe fasts on behalf of the child, but the child can perform fasts at a later time, and according to some the child themselves can perform it if they are able to discern matters.
No, according to the Hanafis. Because they consider it an act of worship and the pen is lifted from a child so they are not required to perform it.
The following is relevant because it is an analogous case: Do children below the age of puberty have to pay zakat?
Ref: الموسوعة الفقهية
Assalam o Allaikum
AFAIK if a person who hasn't reached puberty commits a crime will not be asked for it as he is immature. Following are some proofs for my belief.
Narrated Ali ibn Abu Talib: The Prophet (ﷺ) said: "There are three (persons) whose actions are not recorded: a sleeper till he awakes, a boy till he reaches puberty, and a lunatic till he comes to reason." Source
This Hadith gives us the answer pretty much.
Also, as you said that 'accidentally' there is an ayat that tells us about the actions we do unintentionally, that is:
"....There is no blame on you for what you do by mistake, but ˹only˺ for what you do intentionally. And Allah is All-Forgiving, Most Merciful." Quran 33:5
Rest Allah subhanahu wa ta'ala knows the best.