Can't delete a rigid/flex substack from altium 19
Ran into the same problem myself just a few moments ago (this was an old design imported into version 19).  

Opening the layer stack manager for the 1st time caused my design to gain a sub-stack.  It also was showing an error because both the stacks had the same name.  I changed the name of the sub-stack and that fixed that error, but I still couldn't delete it.

The delete icon was grayed out.

I could add (and delete) further sub stacks.

To revert to just one PCB stack, you need to go to the features drop down box on the top right of the window;  there you will see a tick next to 'rigid-flex'.  Click on the text 'rigid-flex' to turn it off (this is really not the usual intuitive UIF we expect from Altium) and success - the sub-stack (and flex-rigid option) goes away.  

We are now back to the same state the board was in, when it was last opened in an older version (in my case Altium16).