You have free choice. You have free reign with scope and pacing. You tell me.
Let me pop down an example first, and I'll carve those ideas about choice, scope, and pacing out of it at the end.
So let's suppose that Mr. Eastman is going to tear down half of Dry Springs and build an open-pit mine. Brother John and Sister Mary feel this should be stopped, so they confront Mr. Eastman and a conflict begins. The stakes are: does Mr. Eastman come to Pastor Redd's town meeting to make his case?
Mr. Eastman has a honeyed tongue, though, and the Dogs aren't having much success talking him into coming. Sister Mary Gives rather than choosing to Escalate - she's not willing to raise a hand to Mr. Eastman to get him to the meeting, let alone kill and die to see it done. Brother John thinks differently, and rolls up his sleeves to drag Mr. Eastman away, Escalating to Physical.
Mr. Eastman, who has the approximate constitution of an emaciated prairie chicken, pulls his pearl-handled revolver, Escalating straight to Gun.
At this point, Brother John cannot die. He has not yet Taken a Blow during the Gun phase of the conflict - the worst he's at is still d4 from the Verbal phase, since you only update your Fallout based on the Blow you are currently Taking, rather than the progress of the conflict (p.58). He can still Give and roll that d4 Fallout.
Or Brother John can keep going, even Taking a Blow from the revolver and collapsing dead on top of Mr. Eastman after he's been wrestled into coming to that meeting after all. And Sister Mary will probably mourn for him, and she might have been able to treat the wounds if he hadn't rolled a 20, the great lummox. But she didn't get to jump back in - she wasn't willing to go physical to see things done, and Brother John was aware of that but kept going anyway.
So in the example, how could Brother John get hurt? In a Conflict where the stakes explicitly are that Brother John gets hurt, or by Taking a Blow to stay in the conflict and knowingly accepting the risk that it might mean he gets hurt at the end.
In the former case your fellow Dogs are deliberately abandoning you; in the latter, you're deliberately sticking your neck out knowing they can't help you. There is no situation where you get tricked into a fight to the death. You can always walk away, or at least yield and make them decide to chase you.
If Brother John Gives, the Conflict ends and everyone is where they are, having done what they've done. Mr. Eastman isn't going to the meeting, but also Brother John tried to wrestle with him and he's got a gun drawn. He can decide to press the issue, and that would start a new Conflict where the stakes are something like "does Mr. Eastman shoot Brother John?" Sister Mary's free to participate in this Conflict, and she's probably going to want to see it all the way to the end this time.
Scoping conflicts is an important part of running DitV. Especially for initial conflicts, the stakes should be set up such that Giving, Escalating, and Taking the Blow should all be roughly equally on the table. (p.77)
But scope doesn't mean some preset amount of time or space. Scope is however and whatever it takes to settle the question of what's at stake. So, an argument is a conflict and you're probably playing it out roughly in real time, saying the words your characters would say. A barfight is a conflict and you're probably playing it out a little slower than real time, adding some cinematic slo-mo to the action with narration.
But this is also a conflict: can you track the Dulles Gang to their hideout, three days' ride out of town? And this is one too: can you flip a coin, whip out your well-oiled six-shooter (2d6+1d4) and plug it before it hits the ground?
Actions in those conflicts fit their scope. And what was our example scope? Whether or not Mr. Eastman is going to come to the town meeting. Even if guns or weapons are pulled, that doesn't suddenly make it a conflict about one person trying to kill another. It's an argument that suddenly got violent, and isn't going to necessarily have the counterplay of hit-and-get-hit or shoot-and-get-shot that a fight to the death would have.
So, because conflicts can have varying scopes in time and space, the see-and-raise exchanges inside of those conflicts, while they bear some resemblance to the "combat rounds" you might know from other RPGs, are more in the way of narrative beats. They can happen in flashbacks, they can happen over days, they can happen in the blink of an eye.
They can happen with different timing than other see-and-raise exchanges in the same conflict. (p.85 and successive)
That last one is the answer you're going to want to lean into, I think. When it was just talking back and forth all the exchanges roughly tracked the time it took to talk. When it suddenly got violent the exchanges sped up, such that there wasn't an elaborate back and forth between Brother John and Mr. Eastman, but rather a few seconds of struggle and a gunshot, however many exchanges it actually took to get to the end of things.
Or, more generally, it had to happen before Sister Mary could stop it, and you have free reign with scope and narration to work out how. It might be playing out in slightly more than a few seconds in front of her and she's overwhelmed by the joint effort of trying to penetrate the vagaries of Mr. Eastman's elocution and processing the sudden burst of violence from both parties. She might already be down the hall, thinking Brother John would be right behind after Mr. Eastman wore him out and by the time she hears the gunshot it's already too late to stop the dramatic bits.
Now, when I say "you" here, I mean the second-person plural "you". Everyone who's still in the conflict needs to speed up the clock, with probably a little initial prompting from the GM. But that's not really different from how you'd run another kind of conflict, is it? I mean, Sister Mary wasn't going to belt out the Book of Life cover-to-cover as the conflict started - for all that it involves "just talking", it's a bit too big an ask that everyone else should just be inclined to sit there and listen. Similarly now - violence has shown up, but if it doesn't make sense that Sister Mary should sit there and watch it, it needs to be over before she can meaningfully intervene.
Conflicts, exchanges, and this kind of dynamic scoping aren't easy to get your head around, and it's probably going to grate a little on Sister Mary's player to sit there as the conflict plays out, regardless of how much sense it makes that she can't stop it. Can I offer a final desperate plea to not escalate conflicts your fellow Dogs aren't willing to, especially when it might get you shot?