In a multi-sig transaction, if one party refuses to sign, what happens to coins? Are the coins forever lost, or is the transaction voided as if it never was attempted?
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A transaction that is not properly signed is not a valid transaction and thus no different from random junk data. Literally nothing happens. – David Schwartz Jun 12 '16 at 08:56
4 Answers
Only valid transactions transfer control of balances. Since the transaction was never completed, the balances remain under control of the original owners.

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The transaction is not fully signed, so it will not be included in a block, and thus the coins will not be moved from where they are. Only what's in a block can move coins, and anything that causes a transaction to not verify will cause that transaction to not be included.

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voided as if it never was attempted
assuming here you're spending from a multisig wallet and hence >1 parties need to sign. As @user36303 and @Murch♦ pointed out, if the TX is not fully signed, its not really a TX yet and the original balance on this multisig wallet is still the unspent balance.

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It sounds like those two scenarios are the same thing.
If a transaction output requires two signatures to be spent, but one is never available, then the coins on that output aren't going to go anywhere. This is just like where a transaction output only requires a single signature, but it isn't available.
However, this all depends on what type of multisig. For example, if it's a 2-of-3 and one party refuses to sign, then the other two can spend the coins. If it's a 2-of-2, then the coins are stuck.

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Do the "stuck" coins in the unsigned transaction count as spent (and therefore lost) or do they count as unspent? – gm3131 Jun 06 '16 at 22:25
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They are unspent. In this scenario, there is no way to prove that they can never be spent. – Jestin Jun 06 '16 at 22:52
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They would still be unspent, but the rest of the world would know those coins are dead. – Jestin Jun 06 '16 at 23:14
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Wouldn't they know the coins were dead when they were spent elsewhere after the multi sig transaction failed? – gm3131 Jun 07 '16 at 00:56