Transporters work by de-assembling something (e.g. you) and re-assembling it somewhere else. What if, when you’re dis-assembled, you die, and the re-assembled version of you is essentially a copy? Then every time someone steps onto a transporter, their final thought before death is that they’ll end up beamed somewhere else. And the re-assembled version (copy) just thinks that everything went fine and continues on like nothing bad happened.
That’s what they do. This has been a topic in multiple episodes, a fear of multiple characters, and a plot device in a few different stories over the years.