I’m going to call this structural not roofing, I am assuming this eave extension is nailed to the wall framing. I have seen much worse. I am calling it cosmetic, I don’t see it ever falling on someone’s head, but I can’t think of a recommended solution other than call a carpenter.
Any second opinions?

I don’t know but I am more concerned with the gutter down spout. Could not possibly be diverting water 4 ft away from home.

That’s a given

I believe the term in framing is fly rafters or laddering where the gable rafter doesn’t appear supported but you can rest assured its attached via the sheeting and some type of cross
members off the main rake wall framing.
The uneven margin beneath the gutter suggests it is lower than originally built but it probably isn’t going anywhere…

If the client could stand it, a knee brace could be applied where ladder type eave was made. Ladder type eaves kind of suck and tend to sag… you guys get snow up there too, right? I imagine I could push this up with little force.

I don’t think that it has “sagged” I think that it was built that way. Look at the roofing shingles and the spacing between the eave and the roofing shingles.
The so-called “gap” above the roofing shingles has been “filled in” and that appears to be from the original installation.

My “main concern” would be the the water entry points where the gutter & roof shingles meet the siding of the house. If you look closely you will see that there are gaps between the roofing shingles and the siding both above and underneath the rain gutters.