How far back can you verify your Hale line with birth records? Different eras have different answers to each of these questions. Occasionally, census records will make a note if someone living in the household is adopted.
If you think a specific ancestor was indentured, you can try to find the will or estate files of the person they were indentured to. Often, the estate will specify if the indentured person is free to go or if they are to finish their term with someone else.
Another possibility is that somewhere down the line, an unmarried Hale mother had a son by an Akers father, and gave the son her name and he passed it down. Or an Akers fathered a son who was left at an orphanage, and they gave the child the name of Hale. Or someone changed their name for whatever reason and landed on Hale.