If your car's subwoofer is vibrating when the car is off, there could be a few possible explanations for this issue. Here are some potential reasons and steps to diagnose and address the problem:

• Electrical Feedback: Sometimes, electrical feedback can cause the subwoofer to vibrate or produce noise when the car is turned off. This can occur due to issues with the wiring or the amplifier. To troubleshoot this:
  a. Check the power and ground connections for the subwoofer and amplifier. Make sure they are securely connected and not loose.
  b. Inspect the RCA cables and speaker wires for any damage or loose connections. Replace or reconnect them if necessary.
  c. Ensure that the remote wire (usually a blue wire) is properly connected to the amplifier's remote turn-on lead.
• Residual Power: Some modern cars have systems that continue to supply power to certain components even when the car is turned off. This is often the case for radio presets and other memory functions. The subwoofer may be receiving power from such a system. To address this:
  a. Check your car's owner's manual to see if it has any power-saving features that could be affecting the subwoofer.
  b. You may need to install a switch or a dedicated power cut-off for the amplifier to ensure it turns off completely when the car is off.
• Amplifier Settings: If the amplifier's settings are configured improperly, it can cause the subwoofer to vibrate unnecessarily. Ensure that the amplifier's gain, crossover frequency, and bass boost settings are appropriately adjusted for your car's audio system.
• Grounding Issue: A grounding issue can also cause strange behavior in car audio systems, including subwoofers vibrating when the car is off. Check the ground connection for the amplifier and make sure it is securely attached to a clean, unpainted metal surface.
• Remote Wire Issue: The remote turn-on lead that activates the amplifier should only receive power when the car is on. If it's receiving power when the car is off, it can keep the amplifier on. Ensure that this wire is properly connected to a source that is only active when the car is running.
• Battery or Alternator Problems: In some cases, electrical issues with the car's battery or alternator can lead to strange behavior in the audio system. If you suspect this, it's best to consult a professional mechanic.

If you've checked all of these potential causes and the problem persists, it may be a good idea to have your car audio system inspected by a professional car audio technician. They can diagnose the issue more accurately and recommend the necessary repairs or adjustments.