This does not exactly answer the original question, but may prove useful depending on the use case. (And since I wound up here after my search, it may be useful for others.)
In my most recent experience, I'm working with a PATCH api. If a property is specified but with no value given (null/undefined because it's js), then the property and value are removed from the object being patched. So I was looking for a way to selectively build an object that could be serialized in such a way that this would work.
I remembered seeing the ExpandoObject, but never had a true use case for it until today. This allows you to build an object dynamically, so you won't have null properties unless you want them there.
Here is a working fiddle, with the code below.
Results:
Standard class serialization
    noName: {"Name":null,"Company":"Acme"}
    noCompany: {"Name":"Fred Foo","Company":null}
    defaultEmpty: {"Name":null,"Company":null}
ExpandoObject serialization
    noName: {"Company":"Acme"}
    noCompany: {"name":"Fred Foo"}
    defaultEmpty: {}
Code:
using Newtonsoft.Json;
using System;
using System.Dynamic;
                    
public class Program
{
    public static void Main()
    {
        SampleObject noName = new SampleObject() { Company = "Acme" };
        SampleObject noCompany = new SampleObject() { Name = "Fred Foo" };
        SampleObject defaultEmpty = new SampleObject();
        
        
        Console.WriteLine("Standard class serialization");
        Console.WriteLine($"    noName: { JsonConvert.SerializeObject(noName) }");
        Console.WriteLine($"    noCompany: { JsonConvert.SerializeObject(noCompany) }");
        Console.WriteLine($"    defaultEmpty: { JsonConvert.SerializeObject(defaultEmpty) }");
        
        
        Console.WriteLine("ExpandoObject serialization");
        Console.WriteLine($"    noName: { JsonConvert.SerializeObject(noName.CreateDynamicForPatch()) }");
        Console.WriteLine($"    noCompany: { JsonConvert.SerializeObject(noCompany.CreateDynamicForPatch()) }");
        Console.WriteLine($"    defaultEmpty: { JsonConvert.SerializeObject(defaultEmpty.CreateDynamicForPatch()) }");
    }
}
public class SampleObject {
    public string Name { get; set; }
    public string Company { get; set; }
    
    public object CreateDynamicForPatch()
    {
        dynamic x = new ExpandoObject();
        
        if (!string.IsNullOrWhiteSpace(Name))
        {
            x.name = Name;
        }
        
        if (!string.IsNullOrEmpty(Company))
        {
            x.Company = Company;
        }
        
        return x;
    }
}