There was an account of a soldier whose gas mask was pierced by shrapnel while in its case, who only realized it after the gas has already drifted into his trench. The story was related in either Peter Hart's The Great War or G.J. Meyer's A World Undone; I can't quite remember, but I first heard it quoted on Dan Carlin's Blueprint for Armageddon. For that one soldier, there was neither time nor the means to repair his broken gas mask, and he survived by wrestling the mask off of a younger, wounded comrade who was too weak to resist him, causing massive mental trauma to him and a painful death to the other soldier. Earlier in the war, when gas masks were not in common issue yet, troops were ordered to soak cloth in water to cover their noses and mouths as a makeshift form of protection. That may have been an option if you were caught with your metaphorical pants down.

So in short, what a WWI soldier would do if their gas mask was breached would be to panic, and very likely die in agony. Repairs may be made if one wasn't being actively attacked, but once the yellow fog descends you're in for a very bad time.