What does this “their” mean?

“But who’d be that desperate?” he wondered aloud. “If you’re going to
be cursed forever, death’s better, isn’t it?”
“It is,” Firenze agreed, “unless all you need is to stay alive long enough to drink something else –– something that will bring you
back to full strength and power –– something that will mean you can
never die. Mr. Potter, do you know what is hidden in the school at
this very moment?”
“The Sorcerer’s Stone! Of course –– the Elixir of Life! But I don’t understand who ––”
“Can you think of nobody who has waited many years to return to power, who has clung to life, awaiting their chance?” (Harry
Potter and the Sorcerer’s Stone)

I guess ‘their’ does not have a plural meaning here but it is a substitute for his or her. Is this right?

Answer

Yes.

This usage of their as a singular possessive pronoun to replace his or her was uncommon enough to sound jarring and incorrect to me several years ago, but has become very common more recently.

Similarly, they and them are now used as a singular pronoun where he or she and him or her would previously have been used. Even longer ago, the male form alone was used!

This change in common usage is partly because of objections to a former use of he to mean he or she, but to be fair, the use of these plurals as singulars has a very long history indeed, despite none of that history coinciding with my childhood in the UK!

Attribution
Source : Link , Question Author : Listenever , Answer Author : AndrewC

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