Da ging einmal die Tür auf und eine steinalte Frau, die sich auf eine Krücke stützte, kam herausgeschlichen.

The door opened and a stone-aged old woman, who leaned on a cane, slithered out.

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Relative pronouns supply information about a formerly mentioned person, place, thing or idea. "Die" or "who" both refer to the woman. The pronoun borrows the gender and number from woman, but it does not necessarily use the same case.