I heard that several types of slavery existed within human history. One being where a slave's descendants would later be freed and incorporated as members of the ruling society.
Most African slaves were not sent to Europe to begin with; they were sent to the Americas particularly the large plantations of the Caribbean.
Slavery in the Americas moreover was chattel slavery - by and large it was based around devaluing the humanity of the slaves and treating them as cattle. Hence there could be no assimilation between the slaves and slaveowners. This is not the same as Roman slavery, which despite its own brutalities tended to view slaves as a human resource and that highly intelligent slaves were valued for their skills and given avenues for freedom. Intelligent slaves in the Americas by contrast were treated with suspicion and considered to be potential leaders of a slave revolt.
Hence there could be no assimilation to "European society". The slaves instead had to create their own subculture in the Americas; which is why present-day African-Americans have distinct cultural differences from the rest of white America.