Hi --- Your duck isn't sick. She is just deficient in calcium as malformed or soft-shelled eggs are a definite indication of a lack of calcium and possibly other minerals. You need to correct this as it can be FATAL in female birds by leading to egg binding and thus peritonitis.
First, check the ingredient label on your feed. Most commercial diets are formulated around grains fortified with vitamins & minerals. I feed Purina Duck Chow which has enough calcium for male ducks only so I add calcium for the females.
Many will recommend oyster shell. There are three concerns: 1) is the duck eating it? 2) it can contain toxic metals including lead and 3) it is only about 38% calcium. A better source would be eggshells at 94% calcium but they need to be rinsed, sterilized and crumbled. Do you have the time?
The best way to ensure proper nutrition is thru food. Calcium in vegetables is easily absorbed. Everyday you need to feed your duck as much as she wants of one of the following: yogurt, a dark leafy green such as kale, OR dandelion from your yard as long as it is free of lawn chemicals. Also, add black oil sunflower seeds to your daily feed to replace 25 - 30% of it. The calcium content runs about .25% with 16% protein and the 28% fat makes for glossy feathers. It is safe for ALL species including chickens. It will not cause crop binding as the hulls digest. You can read up on black oil sunflower seeds at Feediapedia.org which is an online encyclopedia of animal feeds.
Let me know if you have any questions. And, please think about getting her a duck for company! Take Care!