She stays as Prime Minister, just not leader of the conservative party, until another leader has been elected.
Searching for any updates, sadly I came across this, just posted on the Daily Express website. I take anything by the Express with an extreme pinch of salt, but this came up first
"THERESA May could delay her resignation as Prime Minister until she is confident her replacement as Tory leader can command confidence of the House of Commons, it has emerged."
It goes on to say that if she doesn't like the elected next leader, she will refuse to resign. Surely that would sink the party, if nothing else?
It seems she is completely immoveable!