Newly car always have computer controlled engine which include of O2 sensors, fuel injection system and so on integrated and calculated to produce the efficiency of the engine, how much fuel to the sparkplug and so on. In some car it called ECU
Fuel saver try to save your fuel consumption, for example the hyrogen producing fuel saver that inject hidrogen+oxygen the the air intake and mix with the petrol to make more combustible engine which in turn make fuel lesser for longer distance. Saves fuel. Less fuel more kilometers.
In my opinion and from what i've read. The ECU or computer seeing this phenomena differently. Whenever external substances added and make the engine leaner with less fuel, the computer keep trying to correct the situation by adding more fuel to make engine idle to at the previous state. Because the computer sees this situation as abnormal and try to correct it. So instead of it saves fuel now it consume more fuel.
So after a long time many claims that the fuel saver don't works anymore. It just funtion well at the beginning, it smoothes the engine when idle for example. it saves fuel but now back to previus state.
After reading some articles in internet, There is a guy which uses the HHO technique as fuel saver. He also introduce a method/technique to fools the O2 sensor. The method is to send the false signal to the O2 sensor that eventhough the hho gas injected to the combustion chamber the engine is fine no demand for more fuel, the engine is normal. So by this way the 'fuel saver works. It saves gas.
The method is to troduce simple electronic circuit to the O2 sensor in the middle before it reach to the ECU/computer box.
More info:
EFIE Circuit
In the past, fuel savers would not work when applied to fuel systems with oxygen sensor feedback circuits. These systems were designed to prevent efficient combustion!
Modern fuel systems use an oxygen sensor to maintain a constant air-fuel ratio of the engine. Increasing the combustion efficiency of the engine increases the percentage of oxygen in the exhaust because the engine uses less fuel for the same volume of air and more oxygen is free because the engine produces less carbon monoxide and oxides of Nitrogen.
The increased oxygen content in the exhaust is read by the computer to be a lean mixture in the engine. As a result, the computer then adds extra fuel to bring the pollution back to normal. In other words, when the computer sees extra oxygen in the exhaust, it sends enough fuel to maintain a 14.7 parts air to 1 part fuel ratio. When the computer sees less oxygen in the exhaust, it backs off on the fuel to maintain a 14.7 to 1 fuel ratio. The EFIE's function is to modify the oxygen sensor's output-signal by adding a floating voltage; so the computer will not see the extra oxygen and fight your fuel saver by adding extra fuel.
May this info might help.