See this thread, which is active now:

AA Penalty for Selling My AA Miles

Person trying to sell points lost 300,000 points; another person possibly buying points or ticket (not clear if it's really a relative) had ticket cancelled.

OTOH, there are times one can properly purchase points from the airline, such as American. But that is NOT buying from someone else!

As they say, "Don't even think about it!"

GC