@itskannali
You can attach a resistive load in parallel with your load. In this case you can attach resistor with proper wattage in parallel with your load. When the fuse blows, particularly LED is bypassed and very small mA would flow through the resistor attached in parallel with your load. I don't know if your load is very sensitive that it cannot even sink few mA to operate an LED, that's why I ask you to put resistor in parallel with your load. It completes the loop.
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@Gauthier
I don't even think few mA would damage the load.