Question

What should usually happen if, during a sprint, the product owner identifies a new, important product backlog item (pbi)?

Answer 1

During a sprint, if product owner identifies a new important product backlog item, this has to be discussed with the team in the sprint planning. Based upon the team decision it can be taken in the same sprint or can be moved to next sprint.

Answer 2

the thing that usually happen is The Product Owner adds the new PBI to the Product Backlog
During the sprint, companies usually aimed to enter the market as fast as possible. So they would not have any time to stop and reconstructing previous plan and simply just add new identified item.