To me, it makes sense to have an "emergency contact" field (only visible to site admins) that a user can fill in. I don't think the field should have special semantics ("email address"), some people like me don't read their emails on a perfectly regular basis.

In this day and age, an emergency contact might also be a phone number or even, say, a link to their social media site that permits private messaging. I mean, after all, if the person you are trying to contact would look into their email accounts, there's already a good chance that they would have seen emails sent to whatever address they used on PAUSE or similar.

Plus, an "emergency contact" sort of implies that this could be an emergency that needs to be dealt with as-soon-as-possible. In my mind at least, that could include things like "PM has a very big security problem, it's all hands on deck for gods, site admins and pmdevs". I'm not sure Email has the right reaction time for this sort of thing.

As for dealing with long absence (possible illness or death) of a monk, at least for me it's more likely that some family member or friend would take over my phone to deal with things than it would be for them to find a way to access my email accounts (which run on my own server, shielded by strong passwords). On the other hand, cell phone providers usually have procedures available to take over a dead relatives phone number (call forwarding, etc).