So let's say you are playing a 6-person game. You have 9 points. During Special Building Phase, you reach 11 points. However, you have not won yet because it is not your turn yet.
In the meantime, another player reaches 10 points on her turn. She has beaten you, even though you have more points that her.
From the official Catan FAQ:
Victory Conditions: Can I win during the special building phase?
Answer: No. You can only win during your own turn.
Based on this FAQ, I'd have to believe the answer is yes, but it's the first time I realized it's possible.
I suppose it could also happen during a 4 player game: Let's say you have 9 points. During someone else's turn, the Longest Road is broken up and is transferred to you, putting you at 11 points. However, you have not yet won yet, because it's not your turn. In the meantime, another player reaches 10 points on his turn.