It'll end with a compromise leader finally taking over as these things always do. Unsure who is on the horizon to achieve that, but it is often the case when someone takes over, most of the country, who don't study politics and regularly keep up-to-date on the parties in detail, says, "Who ?"
Meanwhile there is likely to be no agreement between those who want the party to stand for the left wing policies and offer a genuine alternative to the right wing party, for when the country realises it needs a change, and those who'd rather shift further right and be a Conservative Lite party, in the hope that'll result in looking more electable now.
But the Labour party will still continue, as will the country. It didn't all go to pot when the Tories were out of favour and folk were speculating if the Liberals might actually become the second party. It won't for Labour now.