Merriam-Webster's definition of epiphenomenon: a secondary phenomenon accompanying another and caused by it; specifically : a secondary mental phenomenon that is caused by and accompanies a physical phenomenon but has no causal influence itself

Merriam-Webster's medical definition: an accidental or accessory event or process occurring in the course of a disease but not necessarily related to that disease

As regards anencephaly the following is written in Wikipedia: Four recorded cases of anencephalic children surviving for longer periods of time are Stephanie Keene (better known as Baby K) of Falls Church, Virginia, USA, who lived for 2 years 174 days; Vitoria de Cristo, born in Brazil in January 2010 and surviving until July 17, 2012; Nickolas Coke of Pueblo, Colorado, USA, who lived for 3 years and 11 months, and died October 31, 2012; and Angela Morales, from Providence, Rhode Island, who live for 3 years and 9 months, and died December 16 2017.

In almost all cases, anencephalic infants are not aggressively resuscitated because there is no chance of the infant's ever achieving a conscious existence. Instead, the usual clinical practice is to offer hydration, nutrition, and comfort measures and to "let nature take its course". On the other hand, Nickolas smiled when he was touched and it is hard to think that he had no mind. http://www.koaa.com:80/news/medical-miracle-family-treasures-every-moment-with-little-boy-with-no-brain

Infants with anencephaly may have unconscious mind . They have thalamus that is vital in consciousness. Consciousness has been explained well in following two new articles .https://www.researchgate.net/publication/323811734_Conceptual_Advances_in_the_Default_Space_Model_of_Consciousness https://www.researchgate.net/publication/324726707_Top_Mysteries_of_the_Mind_Insights_From_the_Default_Space_Model_of_Consciousness

I think we now need to reconsider 'flat-earth' notions of consciousness, that is merely a phenomenon of the brain and not perhaps a constituent of other phenomenons. I am not an upholder of human 'special nature', which I feel is a religious construct of little genuine value but consciousness may not be simply related to material factors.

This video might help explain an answer

https://www.youtube.com/watch?v=N27XLTuCGoA

We need to open ourselves to new theories that are published in reputed journals . The default space theory of consciousness that we have published has had extensive following . The articles have achieved over 90 th percentile in readership. This is the only theory with 15 new publications in last two years and it is still expanding . It has molecular support as well. To access these articles please click my researchgate site.