It is because of this, you need to take periodic demat statements, print it and file it. No point keeping the statement in email as internet will be doomed in case of ww3. I am sure CDSL or NSDL will have disaster sites across the globe. International Banks maintain disaster sites in different part of the world.
Something similar happened few years ago in Chennai when there was rain/flooding, a colleague like all of us had kept original title deed of property in a locker, the locker was on the ground floor and as it was a big box, the specific locker was on the ground. Continuous rain flooded the branch and water seeped into the locker and everything was pulp when he went to open it.
Although Government department were very helpful, they were saying it would help if he could give some reference number or copy of the title deed to issue duplicate.
The importance of taking important paper copies and filing is important.
Your post made me take my demat copies and place it in a folder. Need to print it out as well at a later date.