No communication between pcm and fuel pump relay

That relay is a simple circuit, thankfully Chrysler just dressed up a Mitsubishi Eclipse for that car. As such you don't have the temperamental Chrysler electronics. The relay get's power on the two Black/white wires on terminals 3 and 4 Terminal 1 goes to the green wire that powers the fuel pump while terminal 4 goes to a black wire that connects to the ECM in connector C111 pin 21. The ECM grounds that pin to turn on the relay which turns on the pump. The relay is in the engine compartment relay box. With it unplugged there should be battery voltage at 2 terminals, you can check that with a cheap test light like the one shown. Those will be one of the large terminals and one of the smaller ones. Then if you connect the test lamp to power and touch the other small terminal you should get the light to turn on as you turn the key on. If you get no light then go to the ECM and terminal 21 and back probe that with a pin or probe kit and see if you get a light there. If you get a light there with the key on then the black wire to the relay is open. A simple overlay would fix that.

The pump is turned on by the key and ECM activating the relay. No other inputs on that system other than an oil pressure switch that tells the ECM to shut off the pump, but it only operates once the engine is running, It gets past a set psi and stays there, it also turns off the oil light or feeds the gauge, so if those work it isn't the switch. Almost has to be the ECM. Did you test if terminal 21 on the ECM is actually providing a ground at the ECM connector itself? If it isn't it's likely a bad driver transistor in the ECM itself.

There was a donate button on the site somewhere. I don't generally go to that part of the site though.
If you want to get your ECU repaired there is a gent named Maic Salazar who does a lot of ECU and other module repairs and he also knows others who repair the ones he doesn't do.
Give him a call and see if he can help you. If you opt for used, be sure that you get the part for the Sebring Coupe, it is not close to the convertible or sedan they sold as Sebring cars. Yours is a Mitsubishi that they dressed up in Chrysler badges while the other 2 are actually fancy K-Cars...
The base part number is MD368988 but the programming depends on the options, OH and FYI you have to use a OE scan tool to reprogram that unit if you go used or new, the aftermarket ones won't write the data correctly thanks to the way the coding was done.
https://www.maicsalazardiagnostics.com/