Well, it was almost a post-mortem. Definitely last rites.
The water heater is a "six-year model" purchased in 1999. The plumber replaced the lower burned-out element in 2002 "under warranty". We replaced it again in 2010. Guess which one was burned out today.
A good element has low resistance (~13 ohms) and is not grounded to the tank. Usually a burned-out element has low resistance but is grounded to the tank. (That's what we had in 2010.) This time the element had infinite resistance... as in no continuity across its terminals.
Last time we just unscrewed the old element and screwed in the new one. This time I got about a quarter turn on the element when water started squirting out. (Hint for new water-heater repair technicians: heater elements go in drywells. "Dry" as in "no water".) So I screwed the element firmly back in and declared "job over".
My neighbor wanted to see the carcass, so we drained the tank and yanked out the element. The water corroded through the drywell, soaked the element, shorted it, and then corroded it. It was probably a few weeks before he noticed that he had a lot less hot water than usual.
I asked him when he'd last replaced the anode rod. He replied "Anode rod?" Now we know what corroded after the anode rod was all gone... most likely the weld joint around the lower element drywell.
We refilled the water heater, set the upper element from 120 degrees to 140 degrees, and turned it back on. He's good as long as he doesn't use more than about 20-25 gallons of hot water at a time. And as long as the upper element holds out.
I was smart enough not to get talked into examining the anode rod. If I tried to take it out of the tank after 13 years of corrosion I'd probably break the tank before I broke loose the threads. When the new heater's installed then I'll show him what's left of the anode rod.
Just go buy a new water heater, right? Not so fast.
The best answer is to go solar but the neighbor wants to re-roof the house. The roof's 23 years old, so it's wise for him to do this before the hurricane does it for him. Once the new roof is on then he can put in a solar water heating system. And as long as he's doing a new roof, maybe he should add in some attic solar exhaust fans plus some radiant insulation.
Now an $11 heater element has turned into a $15K+ re-roofing and solar water project. His spouse is not going to be cooperative. So he's going to balk on buying a new water heater until they finish the roof/solar water discussion. Eventually she'll get tired of lukewarm showers. I predict at least six months of drama.
In a totally unrelated coincidence, a roofer is coming to our house next week to give us an estimate for a silicon coating on our front lanai roof. Now I'm introducing the roofer to two of our neighbors, and possibly a third...
In the early 80s, back when solar water was in vogue, I bought and installed one myself. It has been a while, so I do not remember the exact cost, but I think the panel, pump, and controller were less than $1K (no pipe cost, no labor). Wonder why it costs so much now.
We built ours in 2005 for just over $1000. But that required a lot of used parts (like used panels, a used pump, and a used water heater). I think I bought 60-80 feet of copper piping to wind up through the attic to the roof (and back down again). The controller was the most expensive part because I didn't want to wind toroids all day...
Today's panels are mostly copper, which has become stupid expensive. I don't know if the piping from the heater to the roof can be plumbed in with PEX because the water gets as high as 175 degrees (limited by the controller). We went with soldered copper.
Aside from the price of copper, most of today's expense is the installation labor. Apparently they want properly-trained guys drilling holes into a perfectly good roof to screw 100-pound panels on there.
and I love it. 
