The term "stabilizer" can refer to different devices depending on the context, but assuming you are referring to a voltage stabilizer or a power conditioner that is typically used to regulate voltage fluctuations and protect electronic equipment from voltage surges or drops, it is essential to understand its behavior.
A voltage stabilizer or power conditioner is an active electronic device that requires electricity to function. When it is plugged into an electrical outlet, it draws a small amount of power to operate its internal circuitry, even if the connected appliances are turned off.
The power consumption of a voltage stabilizer while it's in standby mode (i.e., not actively regulating voltage for connected devices) is usually minimal and unlikely to have a significant impact on your electricity bill. However, the actual power consumption can vary depending on the model, make, and efficiency of the stabilizer. High-quality and energy-efficient stabilizers may consume less power during standby.
If you are concerned about energy consumption, you could consider using a power strip or surge protector with an on/off switch to cut off power to the stabilizer (and other connected devices) when they are not in use. This way, you can completely eliminate any standby power consumption when the AC and other equipment are not in operation.