What is our teaching on old age and extending life at any cost?

A non-Catholic family member wishes to keep her mother (my mother-in-law) off life support as she nears death. She is telling the extended family that “Catholics believe in extending life as long as possible at any cost.” and is leaving my wife out of all communications with doctors, signed releases and any decisions. What is the Catholic Church’s teaching on extending life as a person nears death? Is there a reference in the Catechism of the Catholic Church that I can use?

Thank you.

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