What is the ruling on divorcing a wife who fails to fulfill her duties due to illness, and what are the consequences of such a divorce, given that the husband has not yet explicitly pronounced the divorce to her?

The question is unclear, but if the intention is that the husband uttered phrases to his wife ordering her to leave the house, then the husband's saying to his wife: "Leave my house" is not an explicit divorce. Therefore, divorce does not occur by it unless the husband intended it. And merely intending divorce without explicitly uttering it or saying words that imply it, and the husband entering into divorce procedures, does not constitute divorce either. Assuming divorce occurs by the husband's intention, the rights resulting from it vary depending on the condition of the divorced woman.