Keep set -e setting inside || or && - error-handling

Question

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

Answer 1

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