Most Helpful Guy
Yes, but. . . it may cost the two of them their friendship. If not, you may have a problem with your ex saying bad things about you to the new lady. How will you feel when the new lady invites you to a birthday party for one of her friends and you ex is there? It is certainly possible to do this but it presents some unique problems.
Most Helpful Girl
You could if your ex says "Me and you didn't work out and if you can be happy with my best friend go ahead and try" but remember you will see your ex all the time when you hang with friends...
Guys normally would not care of the girl dated their best friend, but girls mind. That would be breaking the girl code.
Girls are more dramatic and emotional and they would feel like you betrayed the friendship...
I would not date my girl-bestfriends ex boryfriend. I could not do it. Only if that happend years after they broke up and if i really loved the dude.