diff --git a/runtime/lib/ffi_native_type_patch.dart b/runtime/lib/ffi_native_type_patch.dart
index 8378e07058da1..edc439509fd75 100644
--- a/runtime/lib/ffi_native_type_patch.dart
+++ b/runtime/lib/ffi_native_type_patch.dart
@@ -7,9 +7,12 @@
 import "dart:_internal" show patch;
 import 'dart:typed_data' show TypedData;
 
+// NativeType is not private, because it is used in type arguments.
+// NativeType is abstract because it not used with const constructors in
+// annotations directly, so it should never be instantiated at runtime.
 @patch
 @pragma("vm:entry-point")
-class NativeType {}
+abstract class NativeType {}
 
 @patch
 @pragma("vm:entry-point")
diff --git a/runtime/vm/compiler/runtime_api.cc b/runtime/vm/compiler/runtime_api.cc
index b5362e880841c..22e9f07d3e223 100644
--- a/runtime/vm/compiler/runtime_api.cc
+++ b/runtime/vm/compiler/runtime_api.cc
@@ -330,6 +330,10 @@ static uword GetInstanceSizeImpl(const dart::Class& handle) {
     case kByteBufferCid:
     case kByteDataViewCid:
     case kFfiPointerCid:
+    case kFfiDynamicLibraryCid:
+#define HANDLE_CASE(clazz) case kFfi##clazz##Cid:
+      CLASS_LIST_FFI_TYPE_MARKER(HANDLE_CASE)
+#undef HANDLE_CASE
 #define HANDLE_CASE(clazz)                                                     \
   case kTypedData##clazz##Cid:                                                 \
   case kTypedData##clazz##ViewCid:                                             \
diff --git a/runtime/vm/raw_object.cc b/runtime/vm/raw_object.cc
index 24a79f89a9a91..9e906cd8ef3b9 100644
--- a/runtime/vm/raw_object.cc
+++ b/runtime/vm/raw_object.cc
@@ -302,6 +302,13 @@ intptr_t RawObject::VisitPointersPredefined(ObjectPointerVisitor* visitor,
       size = RawDynamicLibrary::VisitDynamicLibraryPointers(raw_obj, visitor);
       break;
     }
+#define RAW_VISITPOINTERS(clazz) case kFfi##clazz##Cid:
+      CLASS_LIST_FFI_TYPE_MARKER(RAW_VISITPOINTERS) {
+        // NativeType do not have any fields or type arguments.
+        size = HeapSize();
+        break;
+      }
+#undef RAW_VISITPOINTERS
     case kFreeListElement: {
       uword addr = RawObject::ToAddr(this);
       FreeListElement* element = reinterpret_cast<FreeListElement*>(addr);
diff --git a/sdk/lib/ffi/native_type.dart b/sdk/lib/ffi/native_type.dart
index 61f9cdeb29aef..bd88b282f3ac2 100644
--- a/sdk/lib/ffi/native_type.dart
+++ b/sdk/lib/ffi/native_type.dart
@@ -8,7 +8,7 @@ part of dart.ffi;
 ///
 /// [NativeType]'s subtypes are not constructible in the Dart code and serve
 /// purely as markers in type signatures.
-class NativeType {
+abstract class NativeType {
   const NativeType();
 }
 
diff --git a/tests/ffi/regress_37780_test.dart b/tests/ffi/regress_37780_test.dart
new file mode 100644
index 0000000000000..a6b9f7e8e3076
--- /dev/null
+++ b/tests/ffi/regress_37780_test.dart
@@ -0,0 +1,20 @@
+// Copyright (c) 2019, the Dart project authors.  Please see the AUTHORS file
+// for details. All rights reserved. Use of this source code is governed by a
+// BSD-style license that can be found in the LICENSE file.
+//
+// SharedObjects=ffi_test_functions
+
+import 'dart:ffi';
+
+import 'dylib_utils.dart';
+
+DynamicLibrary ffiTestFunctions = dlopenPlatformSpecific("ffi_test_functions");
+
+final triggerGc = ffiTestFunctions
+    .lookupFunction<Void Function(), void Function()>("TriggerGC");
+
+main(List<String> args) {
+  final foo = [Float(), Double(), Uint8()];
+  triggerGc();
+  print(foo);
+}