Add custom user image field on private messages list instead of default user picture
You have made mistake in your field name, Drupal creates an machine name of any field prefixed as "field_" if you create it using Field UI. Using thumbnail as the style and also ensure that the style you have added -- people_profile_image is created in the Image Styles

so your code should be 

if (!empty($user-&gt;field_profile_image[LANGUAGE_NONE][0]['fid'])) {
  // Load the file
  $file = file_load($user-&gt;field_profile_image[LANGUAGE_NONE][0]['fid']);
  $account = user_load($user-&gt;uid);

  // Note the style name is "thumbnail" and that your field name is
  // field_profile_image not profile_image which you have put in second line
  // which loads the file
  echo theme('image_style', array('style_name' =&gt; 'thumbnail', 'path' =&gt; $file-&gt;uri));
}