no, the skill points won't be given to the player who buys the player, they will disappear and the person who has bought that player will have to start at where the players quality currently is.
with new position skill points, the player who buys a player who is currently being trained to a new position will not get the skill points for the player who is being trained to a new position, and they will have to start all over again.
so yes, all the skill points will be reset.