This question already has an answer here:
I withdrew 3.6 BTC from Poloniex today, but they made the withdrawal transaction without any transaction fee, basically now God knows when it will get to me (basically total loss in day-trading, will NEVER EVER use them again).
Is there anything I can do about this? What happens if it goes to limbo and never gets confirmed?
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The standard transaction fee rules allow for a transaction with no fee to be confirmed if it has high enough priority. This depends on how old the transaction's inputs are; basically, how long since Poloniex received or last transferred those coins.
If it doesn't have high priority, it could still be confirmed, but it depends on the goodwill of the miners. (In principle you could try to convince, or pay, a miner to include it in a block, but I don't know who you might talk to.)
As Tim S. points out in his comment, the priority continues to increase even after the transaction is sent. You can work out from the formula in the above link how long it might take to reach a high priority level.
If it doesn't confirm in a reasonable amount of time, you should go back to Poloniex and ask them to resend it with a fee. They can do this in a way that invalidates the original transaction (essentially a benevolent double-spend) so there would be no risk to them of paying twice. Until you have a confirmed transaction sending you the coins you are owed, Poloniex hasn't fulfilled its obligation to you.
