The answer to your question is that it depends on the aircraft, the flight operation, and what you consider onboard oxygen.
MD88Fan and Alan Hudec have pretty well answered your question. Although I think that you have a slight misunderstanding about the oxygen carried aboard any aircraft. To better understand, let us call the oxygen “Supplemental Oxygen”.
The percentage of oxygen in the air is fairly constant regardless of the useable altitude of most aircraft. At higher altitudes, there is just less air. Less air means that there is less oxygen at the same percentage of oxygen in the air. Just as important is the lower pressure of the air. The lower the air pressure, the harder it is for your body to infuse your blood with oxygen.
At higher altitudes, the only ways to keep your blood oxygenated is to increase the percentage of oxygen reaching your lungs, or to pressurize the air reaching your lungs. Supplemental oxygen can do one or both of these, depending on the supplemental oxygen system. As altitude increases even more, it becomes less possible for the body to infuse even 100% pure oxygen due to the lack of air pressure. That is why a continuous supply of supplemental oxygen can be used in non-pressurized cabins up to a certain altitude.
In a pressurized cabin like the one used for the Airbus family of aircraft, the air in the entire cabin is kept at outside ambient air pressure at and below 8,000 feet MSL Pressure Altitude. Above 8,000 feet MSL Pressure Altitude, the aircraft engine compressors will supply air pressure to keep the inside of the aircraft at 8,000 feet Cabin Pressure Altitude. If the system were to fail, supplemental oxygen is supplied only to the passengers and crew, and not to the entire inside of the cabin.
In a failure of the pressurized cabin and or reduction of cabin pressure, the air crew has pressurized and sealed oxygen masks. The cabin is supplied with portable pressurized masks. The passengers are is normally supplied with chemical oxygen generators that should last about 15 minutes. The oxygen supplied is of a high concentration. But, it is at a minimal increased pressure.
This gives the air crew plenty of time to perform an emergency descent down to 10,000 feet MSL or below, where the outside air pressure is enough to make the air inside the cabin breathable. For comparison, Denver, Colorado has an elevation of over 5,000 feet MSL and Vail, Colorado has an elevation of over 8,000 feet MSL.
The only normal exception to the above are aircraft that have flight paths that require extensive time over very high terrain. Aircraft flying in the Himalayas are an example of this. These aircraft will be outfitted with pressurized oxygen masks supplied by pressurized bottles of oxygen for each occupant on board. These bottles take up useable space and payload capacity. But, they are necessary to provide each occupant both the oxygen, the pressure, and the time necessary for the aircrew to find a safe path down to a lower altitude.