What does this “their” mean?

Question

"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 1

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!