This can vary greatly depending on what was done.
If you do a cross-chain transaction to an asset we support (for example BTC to a BCH address):
Bittrex can recover these funds but they charge a fee to do so, Bittrex charges 0.1 BTC to recover funds.
If the amount sent is less than that it would not make sense to pay this fee in order to recover these funds. Those funds would be considered lost.
If you do a cross-chain transaction to an asset we do not support (for example TNT to a BTC address):
Those funds are considered lost as we do not support the asset and thus cannot recover those funds to your Abra wallet.
If you send your funds to the wrong address entirely, those funds are considered lost.
If you sent your funds to the right address but did not include the correct Tag/Memo