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When Anakin is introduced to the council to be made a padawan, the council finds fear in him.
Part of their reluctance to take him as a padawan is the fear he seems to possess.
Considering the limited number of jedi and the resources they have, I don't think that placing his mother on a safe planet, not enslaved, would have been very difficult.
In general, they take the children very young so they don't get attached to their family. So it's not like they have many families to take care of. And I'm not saying to pay her mother a monthly income, just to move her to a safe place, and free her. She can survive on her own afterwards.
As they took him older, as an exception, it just makes sense to make another exception and help his mother.
Seeing his mother being tortured in his dreams then seeing her die was the first step on the dark side, which could have been avoided very easily.
So considering that he is the "chosen one" and that he seems pretty unstable, why didn't they take care of his mother?