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I understand that 「の」 can be used to indicate possession or to change a noun to a modifier for another noun. But neither of those seems to be the case here.

What usage of 「の」 is being used here?

marked as duplicate by broccoli forest, Dono, oals, Community Apr 28 '16 at 21:17

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終わりのない is not a complete sentence. This phrase can be used as a relative clause which modifies another noun.

  • 終わりのない話 a story which has no end; a never-ending story
  • 終わりがない話 a story which has no end; a never-ending story

As you can see, this type of の is a subject marker (just like が) which can be used only in relative clauses.

See: How does the の work in 「日本人の知らない日本語」?

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