In certain societies that practiced slavery, like crusader Spain or the Ottoman Empire, enslaved people were sometimes able to be bought back by family or communities. Was this ever a possibility for enslaved people trafficked across the Atlantic?
It was possible and it sometimes happened at least with slaves sent to South America and the Carribean. It would have been very rare I imagine but there are examples of it.
For two examples from the Kingdom of Dahomey: One of the princes who would compete against Agonglo for the royal stool was someone who had spent time as a slave in Brazil when he was younger. Also the Kpojito of King Gezo (a sort of Queen-Mother figure) was at least believed to have been bought back from slavery in brazil and returned to the kingdom.
The book "Wives of the Leopard " by Edna G. Bay, goes into detail about the latter and while it is disputed if she was in fact the same woman sold into slavery years prior there are numerous sources cited that at least show it was thought to be possible to redeem people. Several of the missions Gezo sent to the Americas were reported as ordered try to find her and return her if possible.