I know that the ASX makes option adjustments on corporate events that affects shares underlying options in a specific way. Whether any adjustments are made depends mostly on whether it is a pro rata event (ie affects all underlying shares equally).
See
View attachment 43237. Find it by searching for "option adjustments" on ASX website.
The only real exception to option adjustment is dividend announcements.
So if you had tried to short TAH by buying put options prior to the demerger but exercisable after the demerger, the put option would effectively have been split in two, giving a put option over TAH and a put option over Echo at (presumably) half the price.
Quite a lot of money can be made in this way, just see Greenblatt, "You can be a Stock Market Genius". In spite of the title, it is a fascinating and informative guide to special situation investing. Oh and most of the time money is made buying not selling into a demerger

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I presume if you had an open short position through a demerger the process would be the same.
As always this is mere amateur advice, so DYOR.