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That is a very generic question, actually not related to ROS (unless you are talking about an specific ROS package), but I will try to answer it anyway.

Basically, you have to periodically run collision checking on your path, and if the path is not longer valid, recalculate. Depending on the algorithm and your specific problem, you can do this in many many different ways. For example, if you are able to detect what changed in the map, you only have to evaluate if the path goes through those places with changes. Or if the robot is moving along the path, you do not need to check the whole path, just the remaining part. Or if you use a planner like elastic bands or something, it will automatically update to avoid collisions.

At the end, it really depends on what you are using and your problem statement.