What role do hidden fields play in ensuring all checkbox selections are captured in PHP form submissions?

Hidden fields play a crucial role in ensuring all checkbox selections are captured in PHP form submissions by storing the checkbox values in a hidden input field. This allows the checkboxes to retain their values even if they are not selected when the form is submitted. By including hidden fields with the same name as the checkboxes and setting their values accordingly, all checkbox selections can be captured and processed in the PHP form submission.

```php
<form method="post" action="process_form.php">
  <input type="checkbox" name="checkbox[]" value="option1">
  <input type="checkbox" name="checkbox[]" value="option2">
  <input type="checkbox" name="checkbox[]" value="option3">
  <input type="hidden" name="checkbox[]" value="">
  <input type="submit" value="Submit">
</form>
```

In the PHP processing script (process_form.php), you can access the checkbox selections as an array using `$_POST['checkbox']`. This array will contain all the selected checkbox values as well as an empty value for the hidden field, allowing you to capture all selections even if some checkboxes were not selected.