Outer join two tables with null values

I have this data structure:

class Person
{
    public string FirstName { get; set; }
}

class Pet
{
    public int Id { get; set; }
    public string Name { get; set; }
}

class Link
{
    public Person Person { get; set; }
    public int PetId { get; set; }
}

and this data:

List<Person> people = new List<Person>
{
    new Person {FirstName = "Foo"},
    new Person {FirstName = "Bar"}
};
List<Pet> pets = new List<Pet>
{
    new Pet {Id = 1, Name = "FooBoy"},
};
List<Link> links = new List<Link>
{
    new Link {Person = people.First(), PetId = pets.First().Id}
};

Now i want to get the list of all people and their pet names(or null, if there is no pet) The result should be 

Foo - FooBoy
Bar - null

I tried 

var query = from person in people
    join lnk in links on person equals lnk.Person into linkPets
    from link in linkPets.DefaultIfEmpty()
    join p in pets on link.PetId equals p.Id into subPets
    from subPet in subPets.DefaultIfEmpty()
    select new { person.FirstName, PetName = (subPet == null ? String.Empty : subPet.Name) };

But i get null reference exception on link.Pet. If i remove linkPets.DefaultIfEmpty(), i get only the first person.

Jon Skeet
people
quotationmark

Before the question changed

(Originally the link table had a reference to the pet, not an ID.)

It looks to me like you only need one join, because you can just use the Pet property from the link, where there is one:

var query = from person in people
            join lnk in links on person equals lnk.Person into linkPets
            from link in linkPets.DefaultIfEmpty()
            select new { person.FirstName,
                         PetName = link == null ? "" : link.Pet.Name };

After the question changed

I've left the original solution above because it's easy to transform the modified question into the original one - just do a join between pets and links first:

var fullLinks = from link in links
                join pet in pets on link.PetId equals pet.Id
                select new { link.Person, Pet = pet };

var query = from person in people
    join lnk in fullLinks on person equals lnk.Person into linkPets
    from link in linkPets.DefaultIfEmpty()
    select new { person.FirstName,
                 PetName = link == null ? "" : link.Pet.Name };

You could do it in a single statement if you want to, but I wouldn't:

var query = from person in people
    join lnk in (from link in links
                 join pet in pets on link.PetId equals pet.Id
                 select new { link.Person, Pet = pet } )
      on person equals lnk.Person into linkPets
    from link in linkPets.DefaultIfEmpty()
    select new { person.FirstName,
                 PetName = link == null ? "" : link.Pet.Name };

people

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