Capture exit code from pipe command and stdout gets the original outputs.

tee-bash4.4.sh

#!/bin/bash

set -e

OUTPUTSCRIPT="test1"

test1(){
        timeout 3 grep 5 > /dev/null

        echo "found 5"
}

output(){
        if [[ -z "$OUTPUTSCRIPT" ]]; then
                cat
                return 0
        fi

        tee >($OUTPUTSCRIPT | sed -e "s/^/prefix: /")
        wait $!
}

shopt -s lastpipe
shopt -so pipefail

for i in $(seq 1 10)
do
        echo $i
done | output

tee.sh

#!/bin/bash

set -e

OUTPUTSCRIPT="test1"

test1(){
        timeout 3 grep ok > /dev/null

        echo "found 5"
}

output(){
        if [[ -z "$OUTPUTSCRIPT" ]]; then
                cat
                return 0
        fi
        type $OUTPUTSCRIPT > /dev/null
        tee /dev/tty | $OUTPUTSCRIPT | sed -e "s/^/${OUTPUTSCRIPT}: /"
}

shopt -s lastpipe
shopt -so pipefail

for i in $(seq 1 10)
do
        echo $i
done | output