If a Veilwalker remains inside of Veilguard after the Gates close, they become Veilbound, permanently bonded to the realm of Veilguard and unable to leave without disappearing as they pass through the Gate, seemingly vanishing forever. It’s unknown if this is a true death or a transition to another plane of being; the gods maintain that they have never witnessed a Veilbound mortal in any of their afterlives.
Veilbound are effectively the “natives” of Veilguard, forming their own little village within the planar crossroads. It’s unknown if they can have children there, or if they repopulate strictly through Veilwalkers remaining in the realm for one reason or another, and they all get very tight-lipped about such things with anyone who isn’t also Veilbound. What is known is that a number of Veilbound have been documented as living in Veilguard during more than one period of Churning, implying that the Veilbound condition extends a mortal’s lifespan by some amount, possibly indefinitely.