John McDonnell has suggested that Labour could form a minority government if Theresa May's Brexit deal is rejected by the House of Commons, as seems likely. Labour would first have to defeat the Government in a vote of confidence. This would require the support of the Democratic Unionists. That seems unlikely to me, if it meant ushering in even a minority Labour Government. They would be more likely to abstain.
However, let's suppose that Labour did win. The Queen would then send for Mr Corbyn and he would have 14 days to form a minority government. Labour has already held talks with the Scottish Nationalists, although they disagree over freedom of movement. Caroline Lucas would presumably support Labour, as would Plaid Cymru. The Liberal Democrats would certainly demand a second referendum, something that Mr Corbyn does not want. If the Labour Government was defeated on a vote of confidence, there would then be a general election which is what Labour says it wants anyway.
It's an interesting scenario, but an unlikely one. What is possibly being underestimated is the 'Norway for now' option advocated by Nick Boles gaining more traction.