But only someone personally examining them can tell what. They likely are the same joists that bear the floor inside the sliding glass door, so the only thing under the stucco would be blocking. If they are, the exterior portion rotting would concern me that the the rot extends into the interior of the house.

In any case, it will require tearing into it to see exactly what you have going.

The rot appears to not continue into the house. What one of the contractors suggested is that he would flush cut those subs and attach a ledger board across to hold hangers.

I forgot to ask him what the ledger attaches to. Lag bolts into the blocking?

Also thought about sistering up to the stubbed out joists using lag bolts and Simpson ties on the opposite side the new wood is attached. Adding a support beam across the span of the decking joists and of course 4"by 4"'s to the ground moving into free standing. Add a protective coating of some type or other to the joist stub outs to stop deterioration .Than of course build away accordingly.

I use to run a program for that sort of thing no so long ago, feeding in the info.,

The ledger of course the other way, is a standard method and lag bolted into those joists after the flush cut,,so your going use what is already there anyway-see what I mean ?

I can't tell by the pic what the extent of rot or deterioration is ,looking at the stub outs.

And dependant upon how far out your going to bump it out would determine rather it requires support where the deck attach's to your home. Looks like yer bumping out to an 8'by 10' there abouts.

Good luck with your project.