The first question to be addressed is: what is an orphan? In the context of RDBMS, a database table row becomes an orphan when its parent relation is deleted. As an example, suppose you have one table for customers and another table for phone numbers. Each customer can have multiple phone numbers. In the phone number table, you would have a foreign key that refers back to the customer table. If you then delete a given customer, all the related rows in the phone numbers table become orphans.
As we mentioned before, MongoDB is not relational, so such a situation would not arise. A lot depends on good MongoDB database design. Let's look at two approaches that avoid creating orphans: embedded arrays and documents.