Cylinder four misfire?

Hello, since these are two wire coils you can check the resistance of the #4 and compare it with another coil, you can also check the #4 connector for any short to ground, see if you have continuity on either wire to ground with a multimeter. I'll pull up the wiring diagrams for the PCM and the PCM connector pinout for you.

Here are the wiring diagrams for the coils and injectors, along with PCM connector C175E pin 55 is the control wire for coil #4. If you don't find either wire at the coil connector with continuity to ground, plug the PCM back in and check the control wire for a short to ground again. This will check if there's a short to ground through the PCM driver for that coil, I have had them burn the coil drivers out inside the PCM and sometimes there will be a direct path to ground on the control wire. But if the coil shorted out the PCM should have been able to shut down the circuit to prevent damage, but it doesn't always happen that way. I have also had very lean cylinders that cause coils to overheat like this, burning out the coil and the PCM. Just depends on how the fault happened. I assume you had a coil #4 misfire code? P0304?
I would check the spark plug as well.

And thats on the control wire correct? Key Off. Did it blow the fuse yet?
I do hope the driver is ok, you may want to take a look at the Long Term and Short Term fuel trims on a scan tool in the live engine data, if the engine is running lean the fuel trims will be a positive number (is, +15 % for example). That can mean the PCM is compensating for some air/fuel mixture condition by adding fuel. It looks like this is a GDI system as well, so the fuel system is under extremely high pressure, if there are steel fuel lines its a GDI direct injection system, so dont take any fuel lines apart. Just check the fuel trims for now, Hopefully all is ok.

Do you mean if you put a new coil in the #4 cylinder it will melt in 20min? And its not setting any codes at all? Where are you getting these coils from?
And your short to ground is from the coil control wire to battery negative?
If thats all correct, I would see if the #4 injector is intentionally being shut down by the PCM. Or your fuel trims would be all over the place, do you know if this is a GDI system (direct injection)? Do see steel fuel lines going to the fuel injectors or a high pressure fuel pump with steel lines, I dont see a fuel rail pressure sensor in the wiring diagrams, but there seems to be service info for GDI and port fuel injection. Or is there just a "conventional" port fuel injector setup? I would think the PCM is shutting down that injector to protect the Catalytic converter when that cylinder is misfiring, or that injector is not flowing any fuel at all. But we need to know what kind of fuel system it is before testing for injector control, you can take a picture of the fuel injectors if you want and post it here, that will work as well.
I assume youre running the truck with the coil unplugged at this point?

For port fuel injectors, you can check for an injector pulse by connecting a test light to B+ and back probe the injector control wire, the power wires are all the same color on all the injectors, the other wire is the control wire. With the engine cranking or running you should see a dim pulse on the test light. If the test light isnt doing anything that injector is not firing. You can quickly verify power to it on the other wire with the key on as well.

With coil testing, they want you to also check the coil's control wire for a short to power as well as a short to ground. This is the pinpoint testing for the COP coils. If youre melting coils like that, something is very wrong. Id be checking the resistance of each coil as well, make sure they are all about the same.
What Ive seen happen is the PCM driver burned and shorted to ground, the reason the coils over heat and melt is because they are not being pulsed on and off, they are just staying on constantly, so they overheat and will either crack or melt. Id make sure the harness is not making contact somewhere youre not seeing when the PCM is connected, such as melted wires together inside the harness. Im not sure of the testing method used by the company that checked the PCM, but they may have missed something. There has to be code setting if there is a driver problem. That control circuit should not have a path to ground without being trigger on.

https://www.2carpros.com/articles/how-to-test-a-fuel-injector

So the wording of this test is confusing, I can understand that, what we're trying to figure out is if there is power on the control circuit with the coil unplugged, technically speaking this circuit should not have a path to ground without the PCM's coil #4 transistor energized. Following this flow chart it appears they want you to check for voltage at the PCM connector (harness side) with it disconnected, and key On. Its possible for the circuit to be shorted to a "Hot at all times" wire, in which you would read battery voltage (12v) with the key Off. What they are looking for is a key On short to voltage, which could be either 12v or 5v. They should word these things better, hence the reason I dont like flow charts but they do provide some helpful diagnostic steps. So with the coil and PCM unplugged we should be isolating the circuit from everything else.

Looking at the PCM connector pinout diagrams all I see on connector C175E are mostly all sensor signals (inputs) and control driver circuits, having this connector unplugged with the key On may or may not set a bunch of codes, Im sure it will set some circuit fault codes. So after testing, turn the key Off and hook up a scan tool to clear all the codes, then go key off again for a few seconds to make sure they all clear.
If the coil is still plugged in, and key On, at the disconnected PCM connector you will read 12volts. Because youre reading the power coming through the coil to the PCM connector and your other lead is on battery negative. So you want the coil unplugged.

Instead of a multimeter I would use a very low current test light for the first check, many places sell LED test lights for automotive testing now so its safer for PCM circuits, since we dont know what the possible short to power's source is yet. With the PCM disconnected and key On, the other wires for the PCM connecters will be hot and still plugged in, so we want to be as careful as possible with this test.

If its not a bad PCM, we dont want to make it a bad PCM. Using a low current test light will show you its a solid power source the wire is shorted to, but you have to be very careful with the disconnected connector, you dont want to short any power sources in that connector or put power to a circuit that shouldnt have direct power to it.
Once you are sure theres a short to power getting to that wire, you can verify it again with your multimeter, and start to do some wiggle tests on the harness to see if the voltage drops off meaning your close to the short circuit location.

When it comes to wires shorting together, I will check locations of the wiring harness that are "Contact" locations, So where the harness looks like it might be making contact to the engine block or location where its connected to a bracket. The reason being is those locations receive more engine vibration and movement while the engine is running and youre driving.
In some cases where there is high resistance (corrosion) inside a connector or wire, that can be a location where wires start to get hot, wires dont just melt together because they are close to each other. There will be a reason for a wire getting so hot it melts to wires next to it. In your case it could have been the previously failed coil.

Some pins in the connector will show 12volts because some actuators are ground side controlled and now they have power to them with the key On, so until they are actually switched to ground by the PCM and turned on you will read power through them at that connector.

Sorry for the long message, this is just a rare case and we just want to be safe when testing like this. Make sure the key is Off before disconnecting or reconnecting any connectors. And just dont crank the engine with the PCM disconnected. Even a google search gives some further ideas of checking wires for continuity to power wires with the key Off and measuring resistance, the resistance measurement you had before is still concerning, but see what you get here first. Let us know what you find.

This is a great guide to follow as well:

https://www.2carpros.com/articles/how-to-check-wiring

https://www.2carpros.com/articles/how-to-use-a-test-light-circuit-tester