I think if you want to use extension methods you need to use the GroupJoin
var query =
people.GroupJoin(pets,
person => person,
pet => pet.Owner,
(person, petCollection) =>
new { OwnerName = person.Name,
Pet = PetCollection.Select( p => p.Name )
.DefaultIfEmpty() }
).ToList();
You may have to play around with the selection expression. I'm not sure it would give you want you want in the case where you have a 1-to-many relationship.
I think it's a little easier with the LINQ Query syntax
var query = (from person in context.People
join pet in context.Pets on person equals pet.Owner
into tempPets
from pets in tempPets.DefaultIfEmpty()
select new { OwnerName = person.Name, Pet = pets.Name })
.ToList();