Based on the issue description and error traceback, I can generate the fix. The problem is in `sklearn/preprocessing/label.py` at the `transform` method (around line 134). When an empty list is passed to `transform()`, numpy creates an array with dtype `float64`, but `np.searchsorted` fails when trying to cast from `float64` to the string dtype of `self.classes_`.

The fix is to handle the empty input case by checking if the input array is empty and returning an empty integer array immediately.

Here's the patch:

--- a/sklearn/preprocessing/label.py
+++ b/sklearn/preprocessing/label.py
@@ -128,6 +128,8 @@ class LabelEncoder(BaseEstimator, TransformerMixin):
         """
         check_is_fitted(self, 'classes_')
         y = column_or_1d(y, warn=True)
+        if len(y) == 0:
+            return np.array([], dtype=int)
 
         classes = np.unique(y)
         if len(np.intersect1d(classes, self.classes_)) < len(classes):