Organic mulch should not result in plant loss for any reason, unless the mulch is applied too thickly up against the crown or stem of an herbaceous plant. My experience with cocoa bean hulls is that a very young/small annual can succumb to rot if that happens; I assume that the same issue would occur with rice hulls (cocoa bean hulls go through a period of mold growth, which acts as an herbicide and kills small weeds as well as small desirable plants).
Also - a garden mulched with any organic material will hold more moisture than one that is unmulched. I've especially noticed this with cocoa bean hulls, which get soft and mushy when wet (wood chips don't do this). Can it be possible that you are accidentally over-watering, and that the dying plants are in a low spot in your garden? Personally, I don't water mulched Solanaceae family plants unless I'm in a severe drought (two weeks + without any rain).
I've looked into possible diseases that match the symptoms you've listed, and the one that looks like a possible match is verticillium wilt. Here's what The Ortho Problem Solver book says about it:
This wilt disease affects many ornamental plants. It is caused by a soil-inhabiting fungus that persists indefinitely on plant debris or in the soil. The disease is spread by contaminated seeds, plants, soil, and equipment.
The fungus enters the plant through the roots and spreads up into the stems and leaves through the wanter-conducting vessels in the stems. The vessels become discolored and plugged. This cuts off the flow of water and nutrients to the leaves, causing leaf yellowing and wilting.
There is no control available for verticillium - your best bet is to rotate Solanaceae crops over a three-year period and remove all plant debris from the garden (and not into a compost heap) at the end of the growing season. As of 2000, there were no eggplant varieties resistant to the disease.
So - a couple of questions: do you rotate your crops? Is this the first year you've experienced anything like this? If so, did you buy the eggplants at a nursery or store, or did you grow them yourself from seed? Did you add compost from a source outside of your yard?
The white spots on the leaves could be whitefly larvae. View them under a magnifying glass and see if they're tiny insects.