What is this piece

GM had a problem starting in the mid 1970's with camshaft lobes becoming wiped out due to lack of lubrication. The oil that lubes those lobes used to come up hollow push rods, run down the rocker arms, then drain back past the lobes to coat them. They did not put the holes in the right place for oil to be directed to a couple of the lobes, so after a while, they got worn down, those valves would not open, and you would have a misfire.

Even when the design of the engine is okay, the engineers might identify a potential problem caused by failure to change the oil at the proper intervals, or from use of oil with the wrong additives or viscosity. Rather than wait for a failure, then find something to blame it on, the engineers at Ford added these tubes to make sure oil got dumped on the camshaft lobes in sufficient quantity to avoid causing a problem. Adding these tubes is much easier and potentially more effective than redesigning an engine already in production.

Nope. The engine will still run.

Did you find a second half of that tube? If you did, my suspicion would be it wasn't attached firmly, and vibration caused the metal to work-harden, then crack. A crack would typically occur by one of the holes in the tube.

If there is no second half, the engineers meant for oil to be dumped on that cam lobe right below the end of the tube. That seems less likely because what happens to one side of the engine happens to the other side as well, so it has to be addressed the same way. You can see at the very top right of your photo where the tube is crimped closed on the end. The engineers didn't intend for it to be open, so the same would apply to the left side of your photo.

My question now is how big are the holes in the bottoms of those tubes? They're going to dump a pile of oil on those lobes. With this design, there's no other way to get oil up there. GM used hollow push rods. Chrysler used a passage cast into the block on each side that fed oil to hollow rocker arm shafts. Ford used both designs, but this is different. You have "cam followers" under the lobes. Oil runs onto the cam lobes to lubricate the cam followers, then those should flip off most of the oil to prevent overloading the valve stem seals.

Related to this, you must look at how the timing chain gets lubricated. That used to be done with oil that just dripped onto it as it drained back from the cylinder heads at the front of the engine. If the tube in your photo is involved with this, that could explain the sound you were hearing during cranking. This engine uses a system of chain tensioners that add to the complexity and chance of failure. Good lubrication is essential to that system working properly.

This shows how that oil tube bolts to them bearing caps and also a partial part number 6578.

Check the timing chain.