If you're worried about feeding the yeast, you'll probably want to add a little sugar to your recipe. If you keep the amount low enough (I'd probably start with half as much as would usually be used for a given amount of yeast) the yeast will consume all or nearly all of it.
As to cake-like texture, that's as much a factor of lack of gluten development as it is the leavening agent. If you don't have much gluten going, you get that crumbly cake or muffin texture--which is what you want in cakes or muffins.
If you're going to use very little wheat flour or none at all, you might consider adding vital wheat gluten to your recipe so that you can build a decent structure in your bread.
I imagine you'd have to make hundreds of loaves of bread to get the balances right on your own, so I'd recommend looking for low-carb yeast bread recipes that contain a bit of sugar and maybe vital wheat gluten. Those would probably have a decent chance of success.
Without seeing the loaves or knowing your exact procedures, it's hard to guess. My money would be on too dry a dough. Could also be inactive starter, too long a bake, not a hot enough bake, not enough rise time/temperature. So I'll just talk about how I make sourdough in the hopes it'll help. These are techniques I've learned from various books (most notably Reinhart's The Bread Baker's Apprentice) and experiences.
If I did it right, you can click any of the thumbnails for full size images.
First order of business, of course, is having a nice, active starter. I build my final starter from the barm the day before. Depending on my schedule, I either leave it at room temp all night or feed it earlier in the day and pop it in the fridge. It then comes out to warm up a few hours before I bake. It should show strong signs of life. This starter was made with nothing but flour and water--no grapes, no commercial yeast, no juice.
Then comes mixing and kneading. I like to mix the starter with the water first, allowing the starter to break up and dissolve a bit. This ensures good mixing with the final dough. Then I add the flour and salt, mix to a coarse ball...
...and switch to the dough hook for 5 minutes or so. The dough should be stickier than you think it should be. Turn it out onto a floured surface for 4-5 minutes of final kneading by hand to adjust the flour. It should be smooth and supple, still be a bit tacky, and pass the windowpane test. When you stretch it to form a boule, the outside should be smooth and not tear.
Let it rise 3-4 hours at room temp or slightly warmer (a closed oven with a bowl of hot water works well). Then shape and proof for another 3-4 hours.
I start with a very hot oven. 500-550F for artisan loaves. If using a stone, get it in there 45-60 minutes before baking, that way the stone and oven get a good heat soak. Then when the loaves go in, you want to create steam to allow the bread to rise before the crust hardens. A steam pan is a good idea, and I also spray down the walls of the oven with a squirt bottle. Be careful of squirting the light bulb--it will shatter. Don't ask me how I know. After a few squirts, turn the heat down to your final baking temp. I usually go with 450F.
Don't forget to slash them, too. That helps them expand and prevents blowouts. I had some issues getting these guys onto the stone (not my finest hour), but they were still outstanding. You can see the crumb is open and light, but still gelatinized and chewy. Perfect, in my book.
Best Answer
You can't bake bread to end up without crust, as it will always require high temperatures that will toast the outside (to varying degrees) without just dessicating the entire lump of dough.
For pure crustless bread, I would try to make something like a giant steamed dumpling. There are a few examples (courtesy Jefromi and Jay's comments, respectively) of this in Chinese cooking: baozi, a filled dumpling using yeast dough; or the larger mantou, similar but without filling.
When steaming dough it will retain much more (nearly all) water, so a drier dough would be in order. Generally in most bread-baking, the goal as Julio mentions is to get the inside to 200-210 °F, and by using steam at ~212 °F, you will get virtually no browning.
That said, crust can vary wildly, from very soft to very hard. The softer crust breads I bake are usually done in pans at lower temperatures (325-375 °F) and often contain milk, eggs and or fat. The more "crusty" breads are usually baked quickly at hot temperatures (>450 °F), but if done lower and slower it will change the crust significantly.