I wanted to comment and show that this is not an uncommon problem. In my 2011 Outback, I almost duplicated the image that JamesT posted.
The car was not showing signs of a fuel issue except for a slight lag in starting (I thought initially the battery was getting weak). It suddenly died on the highway, and would not restart.
After checking for spark/ignition, I moved on to fuel. There was zero fuel pressure. Upon removing the rear seat and pulling the power connector from the fuel pump, the burned connector was obvious. It got so hot that the metal piece from the pass-through connection (through the fuel filter portion at the top of the fuel pump) melted the plastic around it, and came out with the harness connector.
It is not a comforting thought that I had burning electrical connectors just below my passenger seat and above the fuel tank.
My electrical theory is that the connector became corroded. As the corrosion increased, the resistance also increased, which creates heat at the point of resistance. The fuse did not blow, so there is no failsafe for this situation.
This happens after the warranty has lapsed but really seems like it should be a recall issue.
Replacing the entire wiring harness is not reasonable, so off the junkyard to find a Forester or Outback with the same connector as a donor. Another option is soldering wires directly to the replacement fuel filter/pump. The filter kit is available separately, but hard to find, and a bit of extra labor.
Take a look at the connector on the fuel-tank-side of the filter/flange. I found mine is burned up pretty bad (see image). I bought the filter so that I could rebuild the pump assembly, but now realize I need to get a donor connector for that too. While the fuel to air ratio is probably too rich inside the tank for combustion, this again is not a comforting thought to have burning wires literally inside your fuel tank.