We are given this piece of information at the end of Chapter 14 after Bard has killed Smaug. We are told of the general commotion in Middle Earth after the death of Smaug and how everyone was talking about it. This is how the Elvenking responds:
"That will be the last we shall hear of Thorin Oakenshield, I fear," said the king. "He would have done better to have remained my guest. It is an ill wind, all the same," he added, "that blows no one any good." For he too had not forgotten the legend of the wealth of Thror.
The Elvenking therefore assumes that Smaug had killed the dwarves before Bard manages to kill him and that they perished in the attempt of regaining their treasure.