We're going round in circles.
Things have moved on since the early 1960s.
There are procedures in place now, Truss does not have it in her power to nominate her successor, so your scenario does not hold up.
Brown did not hang on hoping the Lib Dems would see sense, it was established early on that the Lib Dems weren't interested in a Lib/Lab whatever. He hung about while the Tories and Lib Dems haggled over cabinets positions, policy and whatnot, in fact if you read Alistair Campbell's account of that time Brown was forever on the blower telling them to get a move on.
MPs return to their constituencies this weekend, expect cabinet resignations early next week, back bench letters piling up at the 1922 and then the men in grey suits will come calling, but before they do there'll be a quiet coup, the Liz Truss libertarian fruitcakes will be told to shut the fuck up and they'll find a nice Tory corporatist and maybe a one nation Tory side kick to face up the post Truss government.
Remember the majority of the Conservative Parliamentary Party wanted Sunak, it was only the shire Tory fruitcakes that tipped it in Truss's favour.
In such a situation Truss will resign because if she doesn't it'll go to a vote of no confidence in Parliament and no PM wants that humiliation.