Serialize this-types in NativeBehavior separately.

tests/compiler/dart2js/serialization/test_data.dart

Index: tests/compiler/dart2js/serialization/test_data.dart
diff --git a/tests/compiler/dart2js/serialization/test_data.dart b/tests/compiler/dart2js/serialization/test_data.dart
index dd12bfd81b4eb6a9eec793c8a59c604644320034..c32be573e313f2b9b905e742902e4ed9ea369d26 100644
--- a/tests/compiler/dart2js/serialization/test_data.dart
+++ b/tests/compiler/dart2js/serialization/test_data.dart
@@ -631,6 +631,18 @@ test() {
 }
 ''',
   }),
+
+  const Test('Use of dart:indexed_db', const {
+    'main.dart': '''
+import 'a.dart';
+
+main() {}
+''',
+  }, preserializedSourceFiles: const {
+    'a.dart': '''
+import 'dart:indexed_db';
+''',
+  }),
 ];
 
 class Test {