Not meant to be a 'shipped tag, though could be construed as one. Personally, I prefer the vague, 'maybe-maybe-not' relationship the show's writers employed.
(Tag: C*A*V*E)
She's never seen Hawkeye like this before. Hawkeye is never scared, not when awake and fully cognizant. It's almost hard to see him like this, to see the terror in his eyes, the skittishness in his movements, the flatness of the jokes he tries to crack. She's pretty sure it's that, the fact he's unable to laugh this off, that draws her to him. Somehow, as scared as he is, she has an idea what he was like as a child and, despite the shelling, she feels the need to comfort him.
Even here, barely within the cave mouth, she can see how unnerved he is by the situation. He rambles occasionally or, worse, sits silently, his eyes wild as he studies the cave walls. During one of his silences, she tells him her own phobia ("Just as much as you want out, that's how much I want in.") and they laugh together at the vagaries of Fate. She's relieved to see a vague hint of his usual personality in the sound of his laugh; his fear was beginning to transmit to her.
Then, as one particularly close explosion rocks the night, she finds herself in his arms, protected momentarily made protector. Despite BJ's return at about that moment, she doesn't pull away immediately, craving the reassuring warmth of his arms to hold back the terror.
Something in his eyes tells her he understands.