There is no single authority on single and plural pronouns, but our regular grammar expert always has practical advice. In this Talk of Iowa, host Charity Nebbe talks with Patricia O’Conner, author of Woe is I and other books about the English language. O’Conner says "they," "their," and "them" can (sort of) be singular.
She says the arguments for this use: to refer to someone who does not identify as either male or female and doesn't want to be referred to as either "he" or "she," or to refer to indefinite unisex pronouns traditionally considered singular like "everybody," "nobody," and "anybody." O’Conner says that this is one of those cases where grammar has finally come into line with common sense and common usage. Answering listener’s phone call questions, O’Conner also says that a preposition is something you can indeed end a sentence with. Regardless, O’Conner has not changed her thoughts on "irregardless." She doesn’t like it.