Prefix causes empty on 0 fields to not be empty

I'm not sure what you mean by "The prefix/suffix of views", unless you mean the "Use Prefix/Suffix" checkbox in the field in views, which merely appends the prefix/suffix that you set on the field in the Structure->Content Types settings. The only other option I can think of that you mean is rewriting the field with itself and something in front of it (like $[field_price]), which also doesn't work, and is kind of silly to need to do anyway, since that's just duplicating the prefix functionality.

I've attached a series of images (in a .zip for convenience, although I could upload them individually if that's the standard, just not sure) that chronicle these steps:

001: The price field has been added to the Product type. Minimum and default 0, and the prefix is NOT set.
002: An overview of the fields that the Product content type has. Nothing fancy.
003: The Price field in the view. "Display prefix and suffix" is notably unchecked. No results text also displays as "Unavailable", with "0" counting as empty.
004: A product I created called "Hat" that has a price of 0. I also created two others, not pictured here, that have non-zero prices, called "TV" and "Game".
005: The Views preview of the results thus far. Close, but I'd like a dollar sign in front of the prices.
006: The prefix is now set on the Price field of the Product content type. Again, this was done in manage fields. The prefix, for reference, is "$" (not including quotes).
007: As we saw in 003, "display prefix/suffix" is NOT checked. So now, despite being set on the field settings for the content type, it still doesn't show up, because it has not yet been turned on in the view.
008: NOW we turn "display prefix/suffix" on in the view settings.
009: Prices now display with "$" in front - including the price of 0, which (to my mind at least) should count as empty and display "Unavailable".

View query:

SELECT node.title AS node_title, node.nid AS nid, node.created AS node_created, 'node' AS field_data_field_price_node_entity_type
FROM 
{node} node
WHERE (( (node.status = '1') AND (node.type IN  ('product')) ))
ORDER BY node_created DESC
LIMIT 5 OFFSET 0

View code:

$view = new view;
$view->name = 'products';
$view->description = '';
$view->tag = 'default';
$view->base_table = 'node';
$view->human_name = 'Products';
$view->core = 7;
$view->api_version = '3.0-alpha1';
$view->disabled = FALSE; /* Edit this to true to make a default view disabled initially */

/* Display: Master */
$handler = $view->new_display('default', 'Master', 'default');
$handler->display->display_options['title'] = 'Products';
$handler->display->display_options['access']['type'] = 'perm';
$handler->display->display_options['cache']['type'] = 'none';
$handler->display->display_options['query']['type'] = 'views_query';
$handler->display->display_options['query']['options']['query_comment'] = FALSE;
$handler->display->display_options['exposed_form']['type'] = 'basic';
$handler->display->display_options['pager']['type'] = 'full';
$handler->display->display_options['pager']['options']['items_per_page'] = '5';
$handler->display->display_options['style_plugin'] = 'default';
$handler->display->display_options['row_plugin'] = 'fields';
/* Field: Content: Title */
$handler->display->display_options['fields']['title']['id'] = 'title';
$handler->display->display_options['fields']['title']['table'] = 'node';
$handler->display->display_options['fields']['title']['field'] = 'title';
$handler->display->display_options['fields']['title']['label'] = '';
$handler->display->display_options['fields']['title']['alter']['alter_text'] = 0;
$handler->display->display_options['fields']['title']['alter']['make_link'] = 0;
$handler->display->display_options['fields']['title']['alter']['absolute'] = 0;
$handler->display->display_options['fields']['title']['alter']['word_boundary'] = 0;
$handler->display->display_options['fields']['title']['alter']['ellipsis'] = 0;
$handler->display->display_options['fields']['title']['alter']['strip_tags'] = 0;
$handler->display->display_options['fields']['title']['alter']['trim'] = 0;
$handler->display->display_options['fields']['title']['alter']['html'] = 0;
$handler->display->display_options['fields']['title']['hide_empty'] = 0;
$handler->display->display_options['fields']['title']['empty_zero'] = 0;
$handler->display->display_options['fields']['title']['link_to_node'] = 1;
/* Field: Content: Price */
$handler->display->display_options['fields']['field_price']['id'] = 'field_price';
$handler->display->display_options['fields']['field_price']['table'] = 'field_data_field_price';
$handler->display->display_options['fields']['field_price']['field'] = 'field_price';
$handler->display->display_options['fields']['field_price']['alter']['alter_text'] = 0;
$handler->display->display_options['fields']['field_price']['alter']['make_link'] = 0;
$handler->display->display_options['fields']['field_price']['alter']['absolute'] = 0;
$handler->display->display_options['fields']['field_price']['alter']['external'] = 0;
$handler->display->display_options['fields']['field_price']['alter']['replace_spaces'] = 0;
$handler->display->display_options['fields']['field_price']['alter']['trim_whitespace'] = 0;
$handler->display->display_options['fields']['field_price']['alter']['nl2br'] = 0;
$handler->display->display_options['fields']['field_price']['alter']['word_boundary'] = 1;
$handler->display->display_options['fields']['field_price']['alter']['ellipsis'] = 1;
$handler->display->display_options['fields']['field_price']['alter']['strip_tags'] = 0;
$handler->display->display_options['fields']['field_price']['alter']['trim'] = 0;
$handler->display->display_options['fields']['field_price']['alter']['html'] = 0;
$handler->display->display_options['fields']['field_price']['element_label_colon'] = 0;
$handler->display->display_options['fields']['field_price']['element_default_classes'] = 1;
$handler->display->display_options['fields']['field_price']['empty'] = 'Unavailable';
$handler->display->display_options['fields']['field_price']['hide_empty'] = 0;
$handler->display->display_options['fields']['field_price']['empty_zero'] = 1;
$handler->display->display_options['fields']['field_price']['hide_alter_empty'] = 0;
$handler->display->display_options['fields']['field_price']['settings'] = array(
  'thousand_separator' => ' ',
  'decimal_separator' => '.',
  'scale' => '0',
  'prefix_suffix' => 1,
);
$handler->display->display_options['fields']['field_price']['field_api_classes'] = 0;
/* Sort criterion: Content: Post date */
$handler->display->display_options['sorts']['created']['id'] = 'created';
$handler->display->display_options['sorts']['created']['table'] = 'node';
$handler->display->display_options['sorts']['created']['field'] = 'created';
$handler->display->display_options['sorts']['created']['order'] = 'DESC';
/* Filter criterion: Content: Published */
$handler->display->display_options['filters']['status']['id'] = 'status';
$handler->display->display_options['filters']['status']['table'] = 'node';
$handler->display->display_options['filters']['status']['field'] = 'status';
$handler->display->display_options['filters']['status']['value'] = 1;
$handler->display->display_options['filters']['status']['group'] = 0;
$handler->display->display_options['filters']['status']['expose']['operator'] = FALSE;
/* Filter criterion: Content: Type */
$handler->display->display_options['filters']['type']['id'] = 'type';
$handler->display->display_options['filters']['type']['table'] = 'node';
$handler->display->display_options['filters']['type']['field'] = 'type';
$handler->display->display_options['filters']['type']['value'] = array(
  'product' => 'product',
);

/* Display: Block */
$handler = $view->new_display('block', 'Block', 'block');