I honestly don't care for in-person employees, but it's something I ask remote employees to do for this exact reason.
If a remote employee makes vague excuses for why they must keep their old employer on their LinkedIn, it's worth investigating further.
Fortunately it's usually easy to call up the old company and confirm the person's start and end dates. Companies love to learn that one of their employees has started a new job but hasn't actually quit yet.