Car stalls after starting, runs when MAF unplugged

I would say that the camshaft and /or crankshaft position sensors could be failing and the timing is off causing flooding from the timing be so far off. But, that should pull a code.
You can try re-setting the Engine control Module by dis-connecting the battery. That may baseline the ECM, MAF and Fuel Pressure Sensor.
You might also test the fuel pressure manually with a gauge. I could not find a position for a test port, but you can usually find one on the fuel rail. The O2 sensor could cause a lean or rich situation, but if you can smell gas, it might not be that as the amount of fuel delivery change it can do is not that great...but do not rule it out. With the mileage you have replacing the O2 sensor would be a good maintenance idea anyway.
Otherwise I think re-setting the ECM is a good start.

Would disconnecting the MAF disable those other sensor inputs in some way? Remember that the car runs when it is disconnected. So my thinking is that the missing signal from the MAF is keeping the ECU from using input from the actual failing sensor, ll. For some reason the ECU does not recognize the failed part as bad. Apparently not a condition the were testing or expecting.

(SOLUTION BELOW)

I am not certain of that as I did not see any thing to that nature in the service manual I have. The only baseline re-set is to disconnect the battery. This will let the ECM see the MAF and set it to baseline. You may have to drive it for a while before it optimizes the system.

Thanks for the suggestions. I will post my progress.

Aftermarket mass air flow sensors are junk. I have seen it many times on these vehicles. Also to reset the adaptations you can try and to reset it by disconnecting both battery terminals and touching both cables together for about 5 minutes. Also to note, usually small code readers will not pick up some codes in the engine control module. What you can try and do is call your local Volvo dealer to see if they are participating in the Volvo service for life program.

If they scan the system they should pickup a code if there is a fault? But you would need to reset all codes now since there is probably codes for the MAF for signal too high? If there is a fault they should give you a free diagnostic but only covers no more then an hour? But at least you should get a print out of the fault codes and post them here?

If unplugging the MAF sensor makes it run better then I would suspect a faulty MAF nd like I mentioned earlier, aftermarket MAF sensors are really junk. You would need to get one from the dealership but I strongly suggest diagnosing it first since they are expensive. Good luck to you and keep us posted please.

Forgot to provide update. The problem was not in the MAF or any other sensor "failing", but was in the air intake system. I had replaced the radiator and AC condenser in the vehicle. So the turbo intercooler was removed and replaced in this procedure.

Well, the problem ended up being the connection from the intercooler output to the engine intake had separated from the boost pressure. Either I had not tightened the clamp at all or did not tight enough because it was all plastic and I did not want to damage anything.

After closing the gap and tightening the clamp the car is back to full power and running great. Thanks for all of your help. It goes to show a keen eye is one of the best troubleshooting tools you can have.

Thanks for the update and sure makes more sense now. Have seen that problem a few times and as mentioned before Volvo would have picked up the code as a boost pressure fault. I dont know why a small code reader would not pick up the fault? Just makes things harder for the DIY to try and pinpoint the problem. Again thanks for the update and hope we can help you out in the future.

Final update. After closing the air intake leak I still had a symptom of the car cutting out while driving. At idle it would stall, but at highway speeds it would recover and continue to drive.

This seemed like a bad sensor so I systematically started replacing. First, crankshaft sensor was replaced with no effect. Second, camshaft sensor was replaced and it seems like it eliminated the engine cutting out. However a stumbling or hesitation was still felt. Next changed the fuel pressure sensor and it seems to have fixed the hesitation issue.

So after replacing 3 sensors it turns out that 2 were probably failing. I am really disappointed in the diagnostic capability of the ECM. With 2 sensors failing I would expect at least a check engine light even if I cannot read a DTC.