eblo.sh

#!/usr/bin/env bash

set -o errexit

fun-global ()
{
        FOO=$(exit 1)
        echo "fun-global: this won't be printed"
}

fun-local ()
{
        local BAR=$(exit 1)
        echo "fun-local: this *will* be printed"
}

fun-global || fun-local

# % ./eblo.sh
# fun-global: this won't be printed