The $allow_string parameter is not very clearly documented. When true, it simply allows the first parameter to be the name of a class, instead of an object whose class we are interested in.
Some usage examples:
class parent_class {
// objects and methods ...
}
$possible_child_object = new possible_child_class(); // might be an extension of parent_class
$result = is_subclass_of($possible_child_object, 'parent_class'); // valid
$result = is_subclass_of($possible_child_object, 'parent_class', false); // valid
$result = is_subclass_of('possible_child_class', 'parent_class', true); // valid
$result = is_subclass_of('possible_child_class', 'parent_class', false); // not valid
