This is what I've got:

upstream backend {
server unix:/tmp/backend.socket;
keepalive 99;
}

location /v2 {
include fastcgi.conf;

fastcgi_keep_conn on;
# fastcgi_pass unix:/tmp/backend.socket;
fastcgi_pass backend;
}

I checked with strace and it appeared to close the backend connection right away. Perhaps I made a mistake, I'll check again.