Any fuel pump that is failing can make the engine cough or sputter (at least a little) before it totally dies. Good idea from Bill about checking fuel pressure at the rail! How many miles on the car? Doubt the main pump is going unless the car has many miles on it. My 850's pump is original with over 250k on it. Volvo main fuel pumps are very robust and usually last a very long time before crapping out..

At least with 850's it is much more likely to be one of the fuel pump relays than a main pump failure. I gather you replaced the other one. I suggest checking the one under the hood. That one is probably more likely to go because of greater exposure to the elements.