They used as an indefinite subject (sense 2) is sometimes objected to on the grounds that it does not have an antecedent. Not every pronoun requires an antecedent, however. The indefinite they is used in all varieties of contexts and is standard.
They, their, them, themselves: English lacks a common-gender third person singular pronoun that can be used to refer to indefinite pronouns (as everyone, anyone, someone). Writers and speakers have supplied this lack by using the plural pronouns <and every one to rest themselves betake — Shakespeare><I would have everybody marry if they can do it properly — Jane Austen><it is too hideous for anyone in their senses to buy — W. H. Auden>. The plural pronouns have also been put to use as pronouns of indefinite number to refer to singular nouns that stand for many persons <'tis meet that some more audience than a mother, since nature makes them partial, should o'erhear the speech — Shakespeare><a person can't help their birth — W. M. Thackeray><no man goes to battle to be killed. — But they do get killed — G. B. Shaw>. The use of they, their, them, and themselves as pronouns of indefinite gender and indefinite number is well established in speech and writing, even in literary and formal contexts. This gives you the option of using the plural pronouns where you think they sound best, and of using the singular pronouns (as he, she, he or she, and their inflected forms) where you think they sound best.
Examples of THEIR
All the furniture in their house is brand-new.
They are on friendly terms with their neighbors.
The students are seeking to exercise their rights.
The birds have left their nest.
The trees have all shed their leaves.
Their artwork is on display at the museum.
He was angry because of their arriving late.
Origin of THEIR
Middle English, from their, pron., from Old Norse theirra, genitive plural demonstrative & personal pron.; akin to Old English thæt that
: of or relating to them or themselves especially as owners or as agents or objects of an action <their clothes><their deeds>
Headscratcher for THEIR
It's easy to mix up their, they're and there. Their and they're are both forms of the third person pronoun. Their means “belonging to them.”They're means “they are.”There is not related in meaning but means “in that place.” Here is a sentence that uses all three: They're on their way there.