This is a speculative answer, as both comic and series leave the answer vague and mysterious, better befitting dreams.
However, the answer is down to regular human mortals.
You'll note a lot of arrivals and departures on the shore outside the Gate of Ivory. It's not an accident. The ocean is still part of the Dreaming, but it represents the mass of typical random dreams people have. Morpheus can exert will on this space - he finds and collects his gifts for the Three while jumping from dream to dream in the water, and he does dream crafting nearby, plucking elements from the waters perhaps? - but so long as nothing is amiss he doesnt meddle with the entire ocean.
It's also not an accident that the only citizen able to move back and forth at will is the raven. They are all made from human souls, Matthew included, although it's not made clear where Lucienne gets them (in the comics it is Eve's duty to choose souls that become ravens).
So, mortals have their way in, and this naturally means dreams have a way out. In the comic the just freed Morpheus finds a bus to move around in - and Merv Pumpkinhead was driving, which implies all dreamfolk can "hitch a ride" if they're lucky, but whether they have enough power to get where they want is an open question.
The dreams we see doing so are the most powerful ones. The Corinthian is Dreams foremost nightmare, meant to be his magnum opus of a sorts. Which means a lot of time and energy was put into him. Fiddlers Green is a long term myth given it's own form, and a genius loci would certainly have power enough to move at will.
This leaves Gaunt. (Comics wise Jed's dreamscape was taken over by different characters.) The series makes it clear that Gaunt was the last dreamfolk logged visiting Jed, so its very clear Gaunt rode him back to the waking world. Whether Gaunt was strong enough to manifest physically is an open question, but it's clear Gaunt chose to stay with Jed and try to do something better than simply escape, so its ability is moot.
It's likely that Morpheus cannot close the borders without actively harming the Dreaming. Which leaves the main reason of dreams not leaving as fear of Morpheus himself.