The individual have no fault on the things that happen before he was born.
But institutions and groups that have gained advantages and profit with this crimes have responsability for them, especially if those institutions keep using the advantages that they created to keep the system that opress people in place.
A good example would be the slavery in the Americas. The people enslaved and the people who profit from the enslavement are all dead, but the racism created by the slavery still exist today and the advantages that the descendents of slave owners have are very clear to see in Brazil, US and Caribean.
I'm from Brazil the place to where half of all enslaved Africans where bring, and anyone who look at my country can see that Black and Indigenous descendents suffer a lot from the opression created in colonial times, being the vast majority of the poor and subjects to extremely high levels of state violence, while the descendents of the Portuguese Imperial Family and the Colonial Nobility, that were the slave owners, are some of the richiest people in the country, being the owners of the Banks, Big Media coorporations and large landowners or are army Generals, Politicians and Judges that still control the country, so i think they keep the system created back in slavery times in place to keep the power and have part in the crimes against natives, enslaved people descendents and poor immigrants.