Bash – Is it possible to customise the prompt to show the if there are any background jobs

You'd have to leave a colour trailing after the PS1 (start it after > in your example), and then use the bash DEBUG trap to clear the colour before your command was run (but after you press enter in your shell. Try something like this:

shopt -s extdebug
trap "tput sgr0" DEBUG

If you are using bash, you can set the IGNOREEOF shell variable to a number that specifies how many consecutive EOF chars the shell should ignore before treating the EOF as an exit signal. Check the man page for specifics.

However, that triggers before the "there are stopped jobs" message triggers, so you still have the same problem - you get that message, and one more ^D exits the shell.

An alternative is to put the number of shell jobs into your prompt if that number is greater than zero.

For example, an excerpt from my .bashrc:

PROMPT_COMMAND=prompt_command
prompt_command() {
    job_count=$(jobs | wc -l)
    if [ $job_count -gt 0 ] ; then
        prompt_job="[$job_count] "
    else
        prompt_job=""
    fi
}
PS1="...\${prompt_job}..."

After this the shell may look like ...[1] ...

That puts a job count in your prompt if it is greater than zero. This makes it easy to see when you have incomplete jobs and works well (for me) as a visual reminder that jobs are still running.