diff --git a/src/wp-admin/includes/update-core.php b/src/wp-admin/includes/update-core.php
index ec909143dd..fc6681acb3 100644
--- a/src/wp-admin/includes/update-core.php
+++ b/src/wp-admin/includes/update-core.php
@@ -1143,7 +1143,11 @@ function update_core( $from, $to ) {
 		if ( ! $wp_filesystem->exists( $old_file ) ) {
 			continue;
 		}
-		$wp_filesystem->delete( $old_file, true );
+
+		// If the file isn't deleted, try writing an empty string to the file instead.
+		if ( ! $wp_filesystem->delete( $old_file, true ) && $wp_filesystem->is_file( $old_file ) ) {
+			$wp_filesystem->put_contents( $old_file, '' );
+		}
 	}
 
 	// Remove any Genericons example.html's from the filesystem