Demo the unstable bash 4.3.42 trap in the 64-bit Cygwin (cygwin1.dll of April 21, 2016, size 3539372) on Windows 7 Enterprise SP1

t.sh

#! /bin/bash

set -e

function fun() {
    echo fun called
}

trap '
    err=$?
    trap - HUP INT TERM EXIT ERR
    # changing - to "" above stabilizes the trap
    echo starting a trap loop
    for ((i=0; i<10; i++)) ; do
        echo trap loop
        fun
        sleep 1
    done
    exit $err
' HUP INT TERM EXIT ERR

while : ; do : ; done

# $ timeout 2s ./t.sh
# starting a trap loop
# trap loop
# fun called
#
# $ timeout 2s ./t.sh
# starting a trap loop
# trap loop
# fun called
# trap loop
# fun called
# trap loop
# fun called
# trap loop
# fun called
# trap loop
# fun called
# trap loop
# fun called
# trap loop
# fun called
# trap loop
# fun called
# trap loop
# fun called
# trap loop
# fun called

Hmm just observed a "warning" when testing trap "",

$ timeout 2s ./t.sh
./t.sh: line 3: warning: run_pending_traps: bad value in trap_list[15]: 0x1
starting a trap loop
trap loop
fun called
trap loop
fun called
trap loop
fun called
trap loop
fun called
trap loop
fun called
trap loop
fun called
trap loop
fun called
trap loop
fun called
trap loop
fun called
trap loop
fun called