Q&A: What is the proper etiquette when you receive "goodbye money" before leaving Japan?

Question by drj0402: What is the proper etiquette when you receive "goodbye money" before leaving Japan?
This may be best answered by a Japanese native or someone who is currently living in Japan.

While living in Japan, before moving back for good or before going on a long trip somewhere else, sometimes friends and co-workers will give you what I have come to understand as "goodbye money."

I have heard that it is proper etiquette to give back half of this amount to the giver.

How and

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