In a perfect curling match, in every end each player delivers two stones and unless they end up out of play, no one touches the stone after release -- before the hog line.
We rarely live in a perfect world, particularly at our level of play.
So, what happens when a rock is touched (burned)?
The old rules say the rock is removed from play, plain and simple, and that was a good rule with corn brooms and natural ice.
Since then, equipment has improved, ice has improved dramatically, and better teams found situations where it was better to remove a poorly delivered rock if it could be used to advantage by the other team -- like intentional fouls in Basketball, burned rocks became part of the strategy.
... and the rules changed to reverse that trend.
If a rock is burned between the tee at the delivering end, and the opposite hog line by the team delivering the rock, it is immediately removed from play.
If a rock is touched by the opposing team, and it is the rock being delivered, it is redelivered. If not, it is repositioned by the team who delivered it to a "reasonable" position.
The situation last night had to do with a rock between the hog line and the back line.
If a moving stone is touched by the team to which it belongs, the opposite team may:
- Remove it, and reposition any stones affected by it.
- Leave all stones in their final positions.
- Move all the stones to where they reasonably would have stopped had they not been touched.
If a moving stone is touched by the other team, the non-offending team gets to reposition the stones to where they reasonably would have been if there was no infraction.
If the stones are touched by an external force (a falling player from the next sheet, for example), then everything is reset as agreed by the two teams, or the house is reset to before the last stone, and the last stone redelivered -- or the ultimate rule if the teams can't agree, the end is replayed.
The rule is slightly more complex, and you can read the full rules (R8 and R9) here.