A simple helper class that generates a Reorderable List in Unity that can be folded out.

ReorderableListUtility.cs

using UnityEngine;
using UnityEditor;
using UnityEditorInternal;

public static class ReorderableListUtility {

	public static ReorderableList GetListWithFoldout(SerializedObject serializedObject, SerializedProperty property, bool draggable, bool displayHeader, bool displayAddButton, bool displayRemoveButton) {
		var list = new ReorderableList(serializedObject, property, draggable, displayHeader, displayAddButton, displayRemoveButton);

		list.drawHeaderCallback = (Rect rect) => {  
			var newRect = new Rect(rect.x + 10, rect.y, rect.width-10, rect.height);
			property.isExpanded = EditorGUI.Foldout(newRect, property.isExpanded, property.displayName);
		};
		list.drawElementCallback =  
			(Rect rect, int index, bool isActive, bool isFocused) => {
			if (!property.isExpanded) {
				GUI.enabled = index == list.count;
				return;
			}

			var element = list.serializedProperty.GetArrayElementAtIndex(index);
			rect.y += 2;
			EditorGUI.ObjectField( new Rect(rect.x, rect.y, rect.width, EditorGUIUtility.singleLineHeight), element, GUIContent.none);
		};
		list.elementHeightCallback = (int indexer) => {
			if (!property.isExpanded)
				return 0;			
			else
				return list.elementHeight;
		};

		return list;
	}
}

Used like so in a custom Editor:

[CustomEditor(typeof(InspectMe), true)]
public class InspectMeEditor : Editor {
	private ReorderableList list;

	void OnEnable() {
		var stringArrayProperty = serializedObject.FindProperty("stringArrayName");
		list = ReorderableListExtensions.GetListWithFoldout(serializedObject, stringArrayProperty, true, true, true, true);
	}

	public override void OnInspectorGUI() {
		serializedObject.Update();
		list.DoLayoutList();
		serializedObject.ApplyModifiedProperties();
    }

and for reference here's that fictional class that's being inspected:

public class InspectMe: ScriptableObject {
    public string[] stringArrayName;
}

In Unity 2019, the foldout doesn't work properly anymore because ReorderableList caches the element height. It has the ClearCache() method, but it is internal, so it must be accessed through reflection. I use it like this:

1. Get MethodInfo of ClearCache and store it in a static variable:

private static readonly MethodInfo _clearCacheMethod = typeof(ReorderableList)
    .GetMethod("ClearCache", BindingFlags.Instance | BindingFlags.NonPublic);

2. Store ClearCache delegate action and the list itself in instance variables:

private ReorderableList _list;
private Action _clearCache;

3. Create a delegate for the ClearCache method after the list is created:

_list = new ReorderableList(...);
_clearCache = (Action) Delegate.CreateDelegate(typeof(Action), _list, _clearCacheMethod);

4. Use the delegate inside drawHeaderCallback:

bool newValue = EditorGUI.Foldout(newRect, property.isExpanded, property.displayName);

if (property.isExpanded == newValue)
    return;

property.isExpanded = newValue;
_clearCache();

5. I then expose methods that I want to use for the foldout list:

public void DoLayoutList()
{
    _list.DoLayoutList();
}

In Unity 2019, the foldout doesn't work properly anymore because ReorderableList caches the element height. It has the ClearCache() method, but it is internal, so it must be accessed through reflection. I use it like this:

1. Get MethodInfo of ClearCache and store it in a static variable:

private static readonly MethodInfo _clearCacheMethod = typeof(ReorderableList)
    .GetMethod("ClearCache", BindingFlags.Instance | BindingFlags.NonPublic);

2. Store ClearCache delegate action and the list itself in instance variables:

private ReorderableList _list;
private Action _clearCache;

3. Create a delegate for the ClearCache method after the list is created:

_list = new ReorderableList(...);
_clearCache = (Action) Delegate.CreateDelegate(typeof(Action), _list, _clearCacheMethod);

4. Use the delegate inside drawHeaderCallback:

bool newValue = EditorGUI.Foldout(newRect, property.isExpanded, property.displayName);

if (property.isExpanded == newValue)
    return;

property.isExpanded = newValue;
_clearCache();

5. I then expose methods that I want to use for the foldout list:

public void DoLayoutList()
{
    _list.DoLayoutList();
}

This is brilliant! Thank you!