Hi, sorry for the delay in answering as I was offline. No, it is not normal for the bad leg to lie without any movement. Normally, muscles show no activity when the EMG records the muscle activity at rest. But in case of muscle injury or primary nerve injury (which can be present in your case), abnormal muscle activity will be recorded during rest. During activity, a normal muscle will record a positive response during the EMG test but an injured muscle or nerve will not show appropriate response. You can read this up this site.
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MD in Radiodiagnosis