It depends - there are two scenarios possible -
1) Story is half done - nothing is logically complete. PO thinks that it's important to continue with this feature since it is more important than other items in PB - in which case it should get carried fwd to next iteration
2) Story is half done - a portion is logically complete. PO thinks that whatever is complete is okay for now and remaining stuff can be done later, in that case original story should be split in two parts and story for the undone part can move to lower down the product backlog and need not get picked up in next iteration. Story for the done will be considered done.
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