If the UK leaves the EU, and a European person (who is allowed to live in Ireland, but not in the UK) travels to Ireland, what is to stop them illegally travelling to the UK without a hard border?
The Schengen area, on the other hand, guarantees that people can move across borders without border control. Border control is done at the Schengen area borders, whether that be land borders, sea ports, or airports.
A country such as the UK can continue to be part of the Schengen area without being part of the EU. So anyone can fly into Ireland, where the border checks would be carried out.
From there, the person could freely cross the border to the UK, but they would not have the right to live and work there. In order to do so (legally), they would have to apply for a UK visa and work permit.
However, at the moment neither Ireland nor the UK participate in the Schengen area, so border checks will be conducted according to existing agreements between the UK and Ireland. From what I understand, if a person can freely enter Ireland, they can freely enter Northern Ireland. However, from what I hear, there are additional checks when traveling between Northern Ireland and the UK, so the UK can further control who comes from Northern Ireland.
UK's not in Schengen.
Or I mean, Irish citizenship rules are very lax re: US citizens of Irish descent in particular, what was to stop them migrating to the UK en masse while we were in the EU?