I'm just reposting what I had in the other thread.
I know Yu-gi-oh has problems like this, but for VS, everything follows a logical set of rules you can always reference.
For example, in order to play any effect, you must have priority, and the rules specificy exactly when you get priority. Here are the rules that relavent to this question. Pay close atention to 408.2 because that is the one that directly answers your question.*
408.1 As the recovery phase starts, any powers or modifiers that trigger at the start of the recovery phase are added to the chain. Then the primary player gets priority.
408.2 After all players pass on an empty chain, all players must perform the following set of wrap-up actions to end the recovery phase. This is referred to as the "wrap-up" No player gets priority while these actions are taking place or between these actions taking place. Any powers or modifiers that trigger during the wrap-up will be added to the chain at the start of the next turn's draw phase.
408.2a If at least one player has 1 or more endurance remaining, remove all players with 0 or less endurance from the game; otherwise, remove all players from the game that do not have or share the highest endurance total. When a player is removed from the game, all objects that player owns are removed from the game. Any effects that player controls on the chain are negated by the game rules. Objects that player controls but doesn't own revert to their last controller. Continuous modifiers from objects and effects that player controlled are no longer applicable. If only one player remains in the game, the game is over and that player wins. If more than one player remains, the remaining players play another turn.
408.2b Each player may choose one character he or she controls with the stunned characteristic. The primary player chooses first, and then all remaining players make their choices in clockwise order. Choosing a character is optional. Each player then simultaneously recovers his or her chosen character. Then, each player KO's the remaining characters with the stunned characteristic he or she controls. If a character can't be KO'd and was not chosen, it will remain stunned.* 408.2c Each player readies all objects he or she controls.
408.2d Modifiers with the duration "this turn" finish their duration.
408.2e The initiative passes to the person clockwise from the current player with the initiative.