IIRC, they mentioned in the early episodes that there are defectors that are being sought out to be returned. So, when Claire didn't return (and her dead shadow's fingers and teeth removed, so when/if the body turns up it won't be identified), she would be a fugitive that they would be actively looking for. And these are diplomatic crossings, so they won't investigate evey single person on the other side (though they will spy on some). Each side wants something from the other. I don't see a plot hole here.