This week, Sinn Féin President Mary Lou McDonald called on Boris Johnson to authorise a border poll in the event of a no-deal Brexit.
But how do unionists feel? Is there an openness to a united Ireland?
In the House of Commons in 1981, Margaret Thatcher said Northern Ireland was as British as Finchley. She was trying to reassure unionists that their place in the UK was safe.
Forty years on has that relationship changed?
Jim Dornan, a retired consultant from County Down and a unionist, thinks Brexit has "a lot of people questioning where Northern Ireland sits, where Scotland and Wales sit".
"We were brought up to believe that Great Britain was our only future, but now it seems maybe people in Britain don't feel that way as much any more," he said.
It is that perception in certain quarters in England that has also influenced businessman Tim McKane.
"Really it started when I heard the results in one poll that said if Brexiteers had to choose between Northern Ireland and Brexit, they would choose Brexit," he said.
"It made me feel that perhaps we're dispensable.
"In fact I discussed it with my family and thought, 'I don't know what flag I stand under any more? What does it even mean to be British now?'"
'Does the south even want us?'
Is that view widespread amongst unionists? People living and working in Kilcooley in Bangor do not think it is.
Roberta Gray, who grew up on the loyalist Shankill Road, said no one was going to force her to change her nationality.
"Do people in the south even want us?" she asked.
"And do people here want to have to pay to see their GP or have their bins collected?
"I think people are thinking with their hearts and not their heads."
Alison Blayney, the chief executive of Kilcooley Women's Centre, is worried that talk of a Brexit poll is divisive.
"I think to use a knee-jerk reaction on Brexit and have a border poll is very dangerous," she said.
"Let's get over Brexit before we jump from the frying pan and into the fire."
The political editor of the unionist paper the News Letter, Sam McBride, said any suggestion that a softer unionist stance is widespread is way off the mark.
"The fact that even some unionists are starting to think about this is significant, but I think it has been quite oversold in some quarters," he said.
"There is not a massive surge among unionists in considering an Irish unity prospect."
Some unionists are as wedded to their identity as they have always been. Any widening of the debate may depend on what Brexit delivers.