Responding to your topic regarding HMRC documents, I remembered that I had left this (to be answered soon) but had forgotten about it altogether!
I stand to be corrected but my understanding is:
Other than being eligible for registration as British citizen (subject to either parent's settled status) irrespective of their immigration status, don't think there are any other exemptions (with respect to immigration) - because a leave issued in the past makes a UK born child subject to immigration control and therefore subject to all the conditions and requirements associated with the most recent leave issued to the child.
This allowance (eligible to be registered as BC irrespective of immigration status) stems from the Nationality Act and not Immigration Act.