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?
Only valid transactions transfer control of balances. Since the transaction was never completed, the balances remain under control of the original owners.
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.
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.
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.