The second case the inspector send you on is to find a man's loast money. Talk to the guy. Then follow the clues to these areas in this order:

Electronic Store
Bakery
Library
Downtown Soda machine
Talk to a kid with red hair outside the library and check the garbage can to get the Bag item.
The inspector will reward you with the Arm supporter item.
The Rescue:
When the grocer's wife is missing, it is up to you to find her and take her to the hospital. To find her, enter the Cardon Forest area and simply talk to her. This gives you the option to take her to hospital. Talk to her husband to get the Sunlight item.