Why do depressed people feel inappropriate guilt?

Guilt. There is no one easy answer to this question. I can only best describe it as being many feelings of unfinished business that can be explored safely and in depth in psychotherapy.
Guilt. Dynamically speaking, guilt relates to self blame and negative self concept.
Guilt & depression. Thought processes can become distorted with depression. A person may view themselves & their actions negatively & unrealistically. They may feel responsible when bad things happen that don't even fall under their purview. They may be quick to blame themselves & even minor transgressions can become a major focus for them.