I can't say what they will do, but I can share mt experience. I missed an international flight a few years ago, NOT on purpose, very much out of my control, and it took a lot of convincing and multiple agents to get any sympathy. When I ran up to the desk, the agent responded with a $2,800 option to get me on the next plane. I will say I had much better luck on the phone. After speaking with multiple agents in the airport, I walked outside, nearly in tears, and made the call. After much begging, they were able to get me on the next flight, but I was at their mercy. Terrible connections and bad seat, but at least I got where I needed to go. I was on a routing with a lot of options for flights though, so I'm sure having a lot of open space helped me.