to cut out on {someone} is to leave them in haste, often in a manner that disadvantages the person or persons who have been cut out on.
He cut out on us at the last minute, so we have to split the cost of the trip two ways instead of three.
P.S. You can also speak of devices cutting out on someone, where it means to stop working suddenly, again with the implication of disadvantage.
The engine cut out on us when we were half way across the lake.
The radio cut out on us just as the dispatcher was giving us the street address.