I don't think that the oil pump can completely "fail".
And if it did, you would know it, as it would come through the timing cover, and/or 0 oil pressure would sieze the engine.
Apparently it's common for the oil pump gears to crack clean through, and in several places. Mine had 3 clean breaks in the outer gear. It made no noise either. My 4.6 had a bad tick after warm up, so I replaced lifters, and the broken pump. I was sure I had fixed it...nope, still ticked. I just rebuilt the engine, as the cam, main, and rod bearings were bad. I also pinned all 8 sleeves, even though none appeared to have slipped.
I wonder if that broken piece of metal is part of a piston skirt. The skirt(bottom sided)are known to "collapse", bend inward and/or break off, and that would be your noise, and noise that suddenly got worse.
Look at all of them very closely.

 

I don't really have the experience. I've changed heads on multiple engines but have never gone further than that. How would I see that while the engine is still installed? I have the oilpan off right now and the crank exposed I guess a flashlight and look? duh?

 

Look at the bottom of each piston, all the way around it.
Take the spark plugs out, and you can easily rotate the engine with a ratchet and socket on the crankshaft pulley bolt.
With each piston at the bottom of it's stroke, the skirt/lower half of the piston will be below the cylinder(top half will stay in the bore).
With them at the bottom, you can get a good look at each piston. Any break will be visibly obvious. With the piston's shape, the skirts are the lower sides, you'll see it.
Wear can make the skirts "bend" in, but not visibly, the limit is under .010", but if they are worn like that, that will be a weak point.
I'm not saying that's definately where that piece came from, but very possible.
Also look up to the cam bearings. If they are visibly sticking out front or back, they have "walked", and can cause low oil pressure.
That piece of metal does not look like any of the bearing's material.
Is that piece steel/magnetic? As it doesn't look like aluminum.

 

I don't have the piece anymore as my wife tossed it. But if I remember correctly it was iron. I'll look at the pistons when I get home. But for sure something somewhere has to be snapped. The engine would make noise otherwise and remember the noise came with the low pressure light instantly.