The Stop-Moving rule is a rule covering when an effect is allowed to move a card. It supersedes the Lose Track rule and was introduced as part of the Dominion 2019 Errata and Rules Tweaks.
As with the rule version prior to this renamed one, it only pertains to card movement. Other effects related to a card that has been moved elsewhere first by another effect still happen, as long as they are not contingent on the movement that was prevented. However, due to another ruling posted thereto, an effect that won't happen is playing a card, i.e. when you're told to by a card, such as with Vassal or Sailor (the exception being Throne-like cards' replay ability), and the targeted card has been lost track of.
 Official Rules
- An effect can move a card if it specifies where the card is coming from, or if the effect put the card where it is now.
- If a card isn't where the effect would expect it to be, or has moved away from there and then back, it can't move the card.
- Played cards expect to be in play; they can't move themselves if they aren't.
- Gained cards are expected to be where they were gained to, even if this isn't the discard pile.
- Cards in discard piles can be moved even if covered up by other cards; cards on top of a deck can't be moved once covered up.
 Other Rules clarifications
- When you need to get a specific card from your discard pile, if it's on top, you take it without looking through your discard pile. If it's not on top, you can look through your discard pile to get the card. When you get to choose a card from your discard pile, you can look through it even if you know you will choose the top card.
 List of cards that move cards
These cards have abilities that move themselves or other cards. It is not comprehensive; for example, cards that move other cards from their piles, from your hand, and from mats are not included. Cards in italics have been removed.
 Cards that move cards out of play (mid-turn)
- Treasury (2022)
- Herbalist (2022)
- Scheme (2016)
- Hermit (2022)
- Way of the Butterfly
- Way of the Horse
- Way of the Turtle
- Royal Galley
 Cards that move cards out of play (Clean-up)
- Treasury (2011)
- Herbalist (2010)
- Scheme (2011)
- Hermit (2012)
- Way of the Frog
- Merchant Camp
- Prince (2014)
- Walled Village
 Cards that move discarded cards
 Cards that move gained cards
Some cards gain a card directly to somewhere other than the discard pile. See the No Visiting rule. However, some cards move a gained card after it's been gained; these cards can invoke the Stop Moving rule, and are listed here.
 Cards that move trashed cards
 List of cards that prevent cards from moving
These cards stop other cards from moving, so they may not be where an effect would expect it to be.
- Band of Misfits (2020)
- Inheritance (2021)
- Way of the Mouse
- Prince (post-errata)
Even though the rule got renamed, the only actual change from the 2019 errata is that you can still move a card that was covered up in a discard pile.