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 last part about there being two of you reminds me of The Prestige. I won’t go into further detail in case I’d be spoiling it for you, but would encourage you to watch it if you haven’t.