What does Joshi/Robin Wright mean when she asks "what happens if I finish [your booze]?"
Luv has just stolen the bones from the morgue, while K was re-investigating the scene at Sapper's farm. His superior, Lt Joshi, comes to his apartment to tell him about the theft (and murder), and to demand a status update. During the conversation, she helps herself to his alcohol.
After the significant info is exchanged, the conversation slows down (via abrupt cut, @ 51m15s). This exchange occurs:
Joshi: You know, I've known a lot of your kind. All useful, but with you, I sometimes forget. We didn't have any of you where I was a kid. Do you remember anything? Before you were under me, do you have any memories from before?
K: I have memories, but they're not real. They're just implants.
J: Tell me one. From when you were a kid.
K: I feel a little strange sharing a childhood story considering I was never a child.
J: Would it help you share if I told you it was an order?
K: I have one about a toy that I had. A wooden horse.
... K recounts his memory of hiding the wooden horse in the furnace...
J: Little K, fighting for what's his. It's a good one. Look at me. We're all just looking out for something real. [turns her head towards the booze] What happens if I finish that?
K: Shouldn't I get back to work, madam?
J: [chuckles] Check back in after DNAbase.
I'm trying to understand her remark. My interpretation in the moment was that perhaps she was making a pass at K. But, I don't see how that would fit into the rest of the story, if she were sincere. After all, she's the one who gives him the "wall" speech.
What is going on here?
The 'wall speech' is neither here nor there when it comes to Lt Joshi getting some pleasure - as we see from Mariette and other Replicants, there are many models used by humans (and other Replicants) for pleasure without a pregnancy seemingly having occurred since the birth of Dr Ana Stelline. In this respect I believe it is safe to say that even humans that continue to bear a superiority complex over replicants (including keeping 'kind with kind') do not concern themselves with reproductive concepts or any kind of human considerations when using them for the purposes of sex.
With all of that in mind I have never read the Lieutenants intentions as anything other than her taking a pass at K, hence his reasons for shutting down the conversation so quickly. Even Joi picks up on the interaction, discussing it in a later scene at the data centre, asking K whether or not he prefers his 'Madame' to her.
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