I feel forever indebted to you for saving my life, thank you.
After becoming indebted to the mobsters, he was forced to do some very questionable favours.
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People whose lives are saved by others are indebted to them.
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Indebted means to owe someone something. (Money, gratitude)
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It means you owe somebody something. "I am indebted to the bank
for more money than I'm worth." or "I'm indebted to you for saving
my life; I hope I can repay you someday."