What happens when I unassign a backlog item that has progress, from a sprint?

When you unassign a backlog item, the progress of the item will be kept, and you can later on assign it to another sprint to continue work on the item.

Note that all of the work on the backlog item will be credited to the sprint where you complete the item. So, for example, the work will not be included in the velocity for the sprint that you unassign the item from. If you would like some of the work be credited to that sprint, you can split the item instead.