Is it moral to contact a questionnaire participant because of alarming response?
I know I've read something in a research textbook about unexpected ethics problems, but I don't remember where or what it said.

I think you need to contact your ethics committee (or equivalent), preferably quickly, for guidance. If there were enough questions about welfare on the questionnaire to be likely to bring up some sort of similar response, you should probably think about pre-empting it next time and automatically including links to suitable resources. It may be that now you can send out details to all participants (those who left email addresses, or perhaps the original distribution list, depending on how participants were recruited), as a way of offering help without singling them out. If the wording of the email address field requires it (I can't quite make sense of it), you could perhaps do so together with the results of the research, or a preliminary summary of the results...