Here are the current rules for subgames.
506. Subgames
506.1. Some cards allow players to play a Magic subgame. A “subgame� is the game created by the card’s effect. The “main game� is the game in which the spell or ability that created the subgame was played. The main game is suspended while the subgame is in progress. It resumes when the subgame ends.
506.2. Any main-game abilities that trigger while the subgame is in progress aren’t put onto the stack until the subgame is completed.
506.3. To start the subgame, each player removes his or her library from the game face down. It becomes that player’s deck in the subgame. Abilities that trigger on cards being removed from the main game face down will trigger.
506.3a A player’s deck in the subgame may have less than the minimum number of cards. If a player’s deck contains less than seven cards, the player will lose the game as soon as it starts, even if he or she mulligans. (See rule 420, “State-Based Effects.�)
506.4. The subgame proceeds like a normal game. Randomly determine which player goes first.
506.5. All objects in the main game and all cards outside the main game are considered outside the subgame (except those specifically brought into the subgame). All players not currently in the subgame are considered outside the subgame.
506.5a Some effects can bring cards into a game from outside of it. Cards brought into a subgame from a main game are considered to be removed from the main game. Abilities in the main game that trigger on objects being removed from the main game will trigger.
506.6. At the end of a subgame, each player puts all objects he or she owns that were brought into the subgame into his or her library in the main game, then shuffles that library. Cards removed from the game in the subgame are not put into the player’s main-game library. Instead they remain removed from the game in the main game.
Example: If a card was brought into the subgame either from the main game or from outside the main game, that card will be put into its owner’s main-game library when the subgame ends.
506.7. If another subgame is created during a subgame, there can be multiple subgames and main games. Each main game has one subgame, and each subgame has one main game. In this case, some games will be considered both a main game and a subgame at the same time.
506.6 covers your first questions. All cards are returned to the library for the main game except for those removed from the subgame. Those remain removed from the game.
If I have two players who are trying to concede at the same time, I'm probably just going to call it a draw.
However, I have to question your motives here. What exactly do you hope to accomplish?
