I'd agree with Bob that they are cantilevered joists. They likely go into the structure and are nailed to the sides of the joists for the floor inside the house. I think in order to fix them you're going to have to open up the ceiling, or it may be possible to install a header against the structure and use joist hangers to attach that end of the joists. You won't be able to cantilever the deck this way, you'll need to have posts going down to footers on the unsupported side of the deck. I can't tell from the picture if you have any posts now, I suspect you don't because people wouldn't normally cantilever a deck unless they wanted to eliminate the posts.
Edited by JMac (07/25/12 12:54 PM)
Edit Reason: minor correction
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