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As I understand it, a stale (orphan?) block is determined after it is out competed by its sister block. But I can't help but wonder what would happen to the coinbase transaction's output of the stale block.

Although stale block usually is shorter than 4 blocks. It is certainly possible that some transaction might have used the coinbase of a later staled block. Given scenarios when receiver might not be able to wait for 6 blocks of confirmation, it is possible that some recipient might end up having his transaction output invalidated.

For this kind of case, is there a common practice exist to prevent the loss of the recipient (other than 6 blocks of confirmation)? Or is this scenario considered rare enough to be neglected altogether?

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Found the answer on Bitcoin Wiki short after.

The reward for the blocks on the shorter chain will not be present in the longest chain, so they will be practically lost, which is why a network-enforced 100-block maturation time for generations exists.

Since practically no fork can survive longer than 10 block. This enforcement could prevent the scenario described in the question to happen in the first place.

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