Keep set -e setting inside || or &&

I have a simple script with a simple function which can lead to an error. Let's define this function, and make it broken:

brokenFunction () {
    ls "non-existing-folder"
}

If we execute this function in a block detecting if it is broken, it works well:

brokenFunction || printf "It is broken\n"

prints "It is broken"

Now, let's make the function a bit more complex, by adding a correct command at the end :

#!/bin/sh

brokenFunction () {
    ls "non-existing-folder"
    printf "End of function\n"
}

brokenFunction || printf "It is broken\n"

This script prints :

$ ./script.sh 
ls: cannot access 'non-existing-folder': No such file or directory
End of function

while I expected the function to stop before the printf statement, and the next block to display "It is broken".

And indeed, if I check the exit status code of brokenFunction, it is 0.

I tried adding set -e to the top of the script. The behavior is still the same, but the exit code of brokenFunction if called without || now becomes 2. If called with it, the status code is still 0.

Is there any way to keep the set -e setting inside a function called with ||?

EDIT: I just realized that the function in the example was useless. I encounter the same issue with a simple block and a condition.

#!/bin/sh
set -e
{
    ls "non-existing-dir"
    printf "End of block\n"
} || {
    printf "It is broken\n"
}

prints

$ ./script.sh 
ls: cannot access 'non-existing-dir': No such file or directory
End of block

Solution

As written in man bash, set -e is ignored in some contexts. A command before || or && is such a context.

trap looks like a possible solution here. A working alternative to the last script using trap would look like that:

#!/bin/sh
abort () {
    printf "It is broken\n"
}
trap 'abort' ERR
(
    set -e
    false
    printf "End of block\n"
)
trap - ERR

Some things have to be noticed here:

trap 'abort' ERR binds the abort function to any raised error ;
the broken block is executed in a sub-shell for 2 reasons. First is to keep the set -e setting inside the block and limit the border effects. Second is to exit this sub-shell on error (set -e effect), and not the whole script ;
trap - ERR at the end resets the trap binding, meaning the following part of the script is executed as before.

To test the border effects, we can add the previously non-working part :

#!/bin/sh
abort () {
    printf "It is broken\n"
}

trap 'abort' ERR
(
    set -e
    false
    printf "End of block\n"
)
trap - ERR

{   
    false
    printf "End of second block\n"
} || {
    printf "It is broken too\n"
}

prints:

It is broken
End of second block