[Yo-Yo]

There doesn't have to be a border between Ireland and Northern Ireland. The UK could easily come to an agreement with Ireland to continue the open border/open trade policy that is currently in place due to common membership in the E.U.

[Olog-hai]

Never mind the “borderless” situation being due to the Good Friday agreement, which is not EU-brokered. If anyone would be erecting borders after a UK departure, it would obviously be the EU itself, walking all over Ireland’s sovereignty and inserting itself into an agreement that does not concern them.

[River Hawk]

Indeed, if the UK left the EU it could negotiate any deal with Ireland it wanted, including maintaining the status quo. In fact, the UK and Ireland already have an arrangement called the Common Travel Area which provides for open borders in all the British Isles. That’s a bilateral agreement unrelated to the European Union. So they can continue it if both countries want that.
Problem solved.