What is the possibility of a depressurization emergency during a commercial flight where all or some of the oxygen masks fail?
The oxygen system for passengers in an airliner is generally powered by a chemical oxygen generator.
The generator contains chemicals, which when they come into contact with each other, commence a reaction that produces oxygen for a few minutes.
The act of pulling down the mask triggers the contact between the chemicals.
A generator typically serves two or three seats, and each generator is independent of the others on the aircraft. They are not part of a single system with common points of failure.
The panel behind which the masks is opened by a pressure switch, and can also be opened manually.
However the crew will use bottles of oxygen, and the flight crew will use a more complex system that also includes smoke hoods.
Conceivably (anything is possible) a manufacturing fault or sabotage could render every single one of the generator/mask sets inoperative, but it would be an extraordinarily unlikely thing to happen.
People often imagine a system of pipes carrying oxygen to all the masks, but in fact such a system is rarely used. One notable example is the earlier (-100 to -400) variants of the Boeing 747, in which the oxygen is indeed piped. And, apparently, may have not always worked as expected:

The flight crew donned their oxygen masks and manually deployed the passenger oxygen masks.
[...] The PIC was also advised that there appeared to be no oxygen flowing through any of the passenger cabin oxygen masks, however this did not seem to have had any ill effect on the passengers. After the PIC cycled the passenger oxygen switch, a momentary surge of oxygen through the passenger masks was observed.

(from an Australian Transport Safety Bureau report into a November 2001 incident)