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Officials have discussed this one already and look to come back to it in the future. While in the TSN article, the rule is aimed more towards the playoffs, it should be used the entire season.
The cheap shot or message sending type of hits that tend to occur late in a game, once the outcome is in hand, would have a carryover penalty. Ideally this would help prevent players who are losing from going after another player.
If they did then the penalty would carry over to the next game. Not all penalties should have this level of punishment. A simple hooking penalty for example should not. Any harsher penalty should be reviewed after the game to determine if it meets a “cheap shot” penalty.
The TSN article points to Shea Weber and the postgame face plant he put on Henrik Zetterberg. Under such a rule, Weber would have started the next game in the penalty box.
The only issue would be at what point in the game could penalties become a carryover? Obviously any penalty that cannot be served during that game would be included. Getting a two minute penalty with 30 seconds to go could be a carryover if it fails a review.
In order to prevent the cheap shots the time frame would need to be extended. All penalties in the last five minutes would be reviewable for a possible carry over. Remember the goal of this rule is to prevent the cheap shot or supposed “message sending” plays. These plays have injured players. If a longer penalty is a possibility than hopefully players will think twice.