The Remains of the Intended Human Are Their Weakness
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Greed explains the rule after Ed kills him
A Homunculus can be weakened when confronted with the physical remains of the human connected to its creation. Their regeneration and control break down enough that the being can finally be killed.
The Breakdown
The weakness is perfectly suited to 2003's version of the Homunculi. The thing that hurts them most is evidence that the original human existed, died and is not actually the being standing in front of you.
Greed: Freedom Before Humanity
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Breakaway Homunculus · Episodes 30–34
Greed is the first Homunculus to make the faction's internal problem obvious. He has already left Dante, gathered his own group and built an identity around wanting everything precisely because he refuses to belong to anybody.
His claim that he wants immortality is almost redundant. What he actually behaves like he wants is independence.
Why it matters
Greed proves that Dante's Homunculi are not extensions of one mastermind. They can defect, hate one another, make friends and choose goals Dante did not assign them.