Sourdough in Bread Maker?
There are three courses of action for producing sourdough with a bread machine:


Use the bread machine just for mixing dough, then rise and bake it separately.  This will produce the best result, defined as the best texture and strongest sourdough flavor.  In this case, you get to monitor the progress of the sourdough as it is rising, which gives you better control over the results.   With this course, make sure to  start preheating your oven early, because it has to be fully ready when the dough is.  It's heartbreaking to watch helplessly as beautiful sourdough loaves collapse while your oven preheats.  Also, you can throw a handful of icecubes into the oven a minute or two before the bread, to get steam, which gives maximum oven spring and a softer crust. This helps prevent the common problem of dense sourdough.
Do a "cheater" sourdough that incorporates both yeast and sourdough starter.  This is the most hands-off approach, but it won't yield as strong a sourdough flavor results as option one.  Basically, you take a standard bread recipe that uses a poolish preferment, and you replace the poolish with equivalent-hydration sourdough starter, but retain the yeast.  So, you're getting leavening primarily from the yeast, but flavor from the sourdough.  Up to half the flour can come from the starter.  You can gradually reduce the yeast amounts and increase rise time until it's approaching a true sourdough. See recipe below!
Do true sourdough with a bread machine that allows you to program VERY long rise/proofing times.  This is the worst option, because sourdough rise times vary greatly, even with the same starter.  The leavening power of starters also varies from almost as fast as instant yeast, to over 12 hours for a full rise.  I think you'll have a hard time finding a bread maker that can be programmed for the longest times, and because you're relying on a fixed timer, the dough will inevitably be either under-risen or collapsing.   Sourdough can go from under-risen to over-risen and collapsing in as little as 30 minutes.


Cheater Sourdough Recipe derived from Pain Sur Poolish:

Ingredients:


425g/15 oz sourdough starter, fed the night before with equal volumes all purpose flour and water (or about 6.7 oz flour per 8 oz water)
227g/8 oz bread ("Strong") flour
227g/8 oz all purpose flour
200 g/7 oz warm water
1 tsp instant yeast (SAF Red Label)
2 tsp salt
Optional: 1 tsp diastatic malt powder
Optional: 1/4 cup dry milk powder


Procedure:


Mix together dry ingredients, then mix in wet ingredients until incorporated.
Knead about 8-10 minutes on stand mixer speed 2, or until the dough is soft and stretchy. It should be a little wet, but not too much.  
Rise dough for ~45 min-1.5 hours, or until doubled.  If using a bread machine, rise an extra 30 minutes or so, and skip to step 9.
If using oven: start preheating to 500F/260C with a pizza stone in the lower rack
Divide dough in half, and shape into two loaves, making sure not to handle too much as this will remove gas. 
If using oven: coat an inverted aluminum 1/2 sheet pan with pan spray and corn meal, then transfer loaves to pan.  Cover with plastic wrap with the bottom coated in pan spray. 
Proof bread 45 minutes to 1 hour, until it stops rising and a finger leaves a dent in the loaf. 
If using oven: throw a handful of ice cubes into the oven to generate steam, then slash the loaves and load into oven.
In oven: Bake @ 500F/260C for 5 minutes, then reduce heat to 435F/225C and bake for a further 15 minutes.  In bread machine: bake at about 375F/190C for about 30 minutes.  If not using diastatic malt, crust may still be somewhat pale.


This recipe (with slight modifications) is now my standard bread, which I bake frequently.  I'm still tweaking the exact time to bake at the reduced temperature; if the top is browning excessively but the interior is underdone, it may help to flip the loves over for the last few minutes of cooking.