How to use detect failure in command substitution - bash

Question

As you know set -e is very useful to discover any failure when command is executed. However I found it to be delicate to use and I don't know how to use it in the following scenarios:
==============First example================================
set -e
function main() {
local X1="$(exp::notdefined)"
echo "Will reach here : ${LINENO}"
X2="$(exp::notdefined)"
echo "Will not reach here : ${LINENO}"
}
main
==============Second example================================
set -e
function exp::tmp() {
echo "Now '$-' is "$-" : ${LINENO}"
false
return 0
}
function main() {
X1="$(exp::tmp)"
echo "Will reach here : ${LINENO}. '\$X1' : ${X1}"
X2="$(set -e ; exp::tmp)"
echo "Will not reach here : ${LINENO}"
}
main
===============================
The first example shows that, if we use command substitution on a local variable, then it will not fail even if the command substituted is not found. I don't know how to detect these kinds of failures.
The second example shows that, if the bash options (-e) will not propagate unless we call set -e inside the command braces. Is there any better way to do this?

Answer 1

You request immediate exit on pipeline failure with -e, e.g.:
-e Exit immediately if a pipeline (which may consistof a single simple
command), a list, or a compound command (see SHELL GRAMMAR above),
exits with a non-zero status.
The reason the bad command substitution does not cause failure within the function is because local provides its own return status.
local [option] [name[=value] ...]
... The return status is 0 unless local is used outside a function, an
invalid name is supplied, or name is a readonly variable.
The assignment of a failed command substitution does not cause local to return non-zero. Therefore, no immediate-exit is triggered.
As far as checking for a failure of command substitution following local, since the output is assigned to the variable, and the return will not be non-zero in the event of command substitution failure, you would have to validate by checking the variable contents itself for expected values for success/failure.

Answer 2

From the bash manual:
Subshells spawned to execute command substitutions inherit the value of
the -e option from the parent shell. When not in posix mode, bash
clears the -e option in such subshells.
Example 2 behaves differently when bash runs with --posix; however for example 1 I can't find any documentation explaining why local would cause this.