If Blitzcrank is played to a battlefield, targets an enemy unit with its WYPM ability, then is returned to base with Flash in response, does the enemy unit get moved into the controlling player's base (creating a broken game state)?

Ruling: The move does not happen because an opponent's base is not a valid destination for a move. Rule 140.1.a.1 defines valid locations for moves and does not include other players' bases.

Nuances:

• Rule 425.2.b states that if a unit would move to a location where it cannot exist, it instead recalls, but this may not apply if the destination itself is invalid for moves
• The "here" reference in Blitzcrank's ability is programmatically determined (not a target), but the destination must still be a valid move location
• Rule 143.4 restricts standard moves from battlefield to another player's base, but this specific restriction only applies to standard moves
• A unit you don't control being temporarily in your base appears to have some support from Hostile Takeover's wording, though that card is designed to minimize such situations