The Post Office couldn’t care less. Eventually, they’ll return it to the sender. Consequences and chain reaction would depend on who sent it, and what it is. You probably have a better idea of that than we do.
The short answer is that the letter will be returned to the sender, annotated to the effect that delivery was attempted, but was unsuccessful.
The longer answer is, obviously, that it depends upon what the letter is. If it’s a notification from the manufacturer of your car, telling you about a recall, you’ll never know about it, your car will catch fire, and you’ll die in a massive ball of flame. If it’s a notification from your homeowner association that, if you don’t pay your dues within the next 30 days, they’re going to put a lien on your property, and then foreclose, you’ll end up homeless.
Certified mail is rarely junk mail, since it costs an extra $2.30 to send it (beyond the 37 cents postage). There are some things that must, by law, be sent by certified mail.
So, how do you know you don’t want it, if you don’t know what it is?