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My textbook states that sometimes, both この and その can be used to refer to the previous sentence.
Some examples:
先週木村さんという人に会った。{この、その}人は大学の先生だ。
私は子供の頃、よく近くの広場で遊んだ。しかし、{この、その}場所はもうない。
アメリカで新しい薬が開発された。{これ、それ}はガンにきくそうだ。
Is there a meaning difference between the two?
There are also 「その」and「どの」 and together they make up what's known as 「こそあど言葉」. But since those two are outside the scope of the question, let's just look at 「この」「これ」「ここ」「その」「それ」「そこ」.
この/これ/ここ：You use this when you have physical or emotional closeness to the thing or person at issue, and it also indicates you are closer to that thing/person than the other party in the conversation.
その/それ/そこ：You don't have that kind of attachment or affinity with the thing under discussion. The topic is closer to the listener.
先週木村さんという人に会った。その人は大学の先生だ。
I don't see a reason to choose 「この」in this sentence. You don't feel close to someone whom you just met and whom you have to refer to as "a person called 木村さん".
私は子供の頃、よく近くの広場で遊んだ。しかし、その場所はもうない。
It's gone. You can't point to it and say "this place". Time separates you from that place in your memory.
アメリカで新しい薬が開発された。それはガンにきくそうだ。
You have either heard this from people or read this somewhere. You don't have any closeness to what's talked about. This sentence suggests the speaker isn't in アメリカ where the new medicine has been developed.
