#!/bin/bash
if [[ -n "$1" ]]; then
    sleep 1 &
    p=$!
    kill $p &> /dev/null
else
    sleep 1 &
    p=$!
    kill $p &> /dev/null
    /bin/true # This line is the sole difference.
fi

$ ./a.sh
/a.sh: line 16: 18103 Terminated              sleep 1
$ ./a.sh foo
$ # no "Terminated" message

#!/bin/bash
if [[ -n "$1" ]]; then
    sleep 1 &
    p=$!
    kill $p &> /dev/null
    /bin/echo "a line"
else
    sleep 1 &
    p=$!
    kill $p &> /dev/null
fi

$ bash ./mystery.sh
$ bash ./mystery.sh foo
a line
./mystery.sh: line 11: 10361 Terminated              sleep 1

$ bash ./mystery.sh
$ bash ./mystery.sh foo
a line

if [[ -n "$1" ]]; then
    sleep 1 &
    p=$!
    kill $p &> /dev/null

$ strace -s 1024 -e kill bash mystery.sh
kill(9830, SIGTERM)                     = 0
mystery.sh: line 11:  9830 Terminated              sleep 1
--- SIGCHLD {si_signo=SIGCHLD, si_code=CLD_KILLED, si_pid=9830, si_uid=1000, si_status=SIGTERM, si_utime=0, si_stime=0} ---
+++ exited with 0 +++
$ strace -s 1024 -e kill bash mystery.sh  foo
kill(9839, SIGTERM)                     = 0
+++ exited with 0 +++

$ strace -s 1024 -e kill,wait4 bash mystery.sh  foo
kill(9910, SIGTERM)                     = 0
+++ exited with 0 +++
$ strace -s 1024 -e kill,wait4 bash mystery.sh
kill(9916, SIGTERM)                     = 0
--- SIGCHLD {si_signo=SIGCHLD, si_code=CLD_KILLED, si_pid=9916, si_uid=1000, si_status=SIGTERM, si_utime=0, si_stime=0} ---
wait4(-1, [{WIFSIGNALED(s) && WTERMSIG(s) == SIGTERM}], WNOHANG, NULL) = 9916
wait4(-1, 0x7ffe8e5bb110, WNOHANG, NULL) = -1 ECHILD (No child processes)
wait4(-1, [{WIFEXITED(s) && WEXITSTATUS(s) == 0}], 0, NULL) = 9917
mystery.sh: line 11:  9916 Terminated              sleep 1
--- SIGCHLD {si_signo=SIGCHLD, si_code=CLD_EXITED, si_pid=9917, si_uid=1000, si_status=0, si_utime=0, si_stime=0} ---
wait4(-1, 0x7ffe8e5bb250, WNOHANG, NULL) = -1 ECHILD (No child processes)
+++ exited with 0 +++

#!/bin/bash

## ... copy code from the question above.

sleep 0.2