About the Jones' Situation:
Beginning Tuesday, all teams were permitted to place as many as seven players per day on the waiver wire. Thus by Friday, many teams will have already put members of their 25-man roster on waivers.
Multiple teams can claim a player who has been placed on waivers. If two teams were to claim a specific player, the lower-ranking team according to winning percentage (whether it be an American or National League team), is given rights to that player for 48 hours.
If the Astros and Red Sox were to both put a claim on Andruw Jones, the Astros would have that 48-hour period to discuss a trade with the Braves. If nothing materialized, Jones would remain with the Braves.
All players remain on the waiver wire for two full business days. If they are never claimed, they can be traded at any point, to any team for the remainder of the season. But to be eligible for the postseason, a player must be traded by Aug. 31.
If a player is claimed by a team and a deal never materializes, a team will not likely place them back on waivers. When they initially place a player on waivers, a team has the right to pull them back at any time.
But when a player is placed on waivers a second time, the claim is irrevocable. Thus any claiming team owns the rights and a trade must be completed.