PHP: Why isn't exec() returning output?
Solution 1:
You should redirect stderr to stdout.
To do that, change your exec() call like this:
exec("ping -c 1 $domain_bad 2>&1", $output, $return_var);
More info about 2>&1 meaning here.
Solution 2:
If the answer above could not solve your problem, maybe exec() is disabled. You can try to check php.ini file at disable_functions line.