Try setting this variable to non-nil:
(setq org-export-with-broken-links t)
Thanks for the tip here! This is definitely close to what I want. I think I'm going to need to code up something additional though in that none of the default options (mark or ignore) are really the behavior that I want.
- mark: I don't like the way the text comes out here. I don't want to have BROKEN LINK in the exported text at all.
- ignore: I don't like how the text of the link simply disappears in this case.
What I really want is something that keeps the link text but drops the link, essentially converting it into plain text (or stylized text if the link text is in markup).
I'll have to play around with how to do that.