Workflow that Automatically Close Cases after a certain Number of Days after Last Modified Date

A. Create a case search to filter the cases that should auto-close.
1. Navigate to Lists > Search > Saved Searches > New.
2. Click Case.
3. Enter criteria based on business needs. Ex:

• Status is In Progress
• Date Last Modified is on or before 30 days ago

4. Click Results tab.
5. Add/Remove fields based on need but make sure that Status is one of the fields.
6. Check the Public check box.
7. Enter a name in the Search Title field. (Ex. Case for Auto-Close)
8. Save.

B. Create a workflow.
1. Navigate to Customization > Scripting > Workflow > New.
2. Enter a Name for the workflow.
3. Select Case in the Record Type field.
4. Check Execute as Admin check box.
5. Set the Release Status to Released.
6. Click the Scheduled radio button under Initiation.
7. Select the saved search from A in the Saved Search field.
8. Click Save.
9. Click New State button.
10. Enter a name for the new state.
11. Save.
12. Click the state button in the Diagram.
13. Click New Action button on the Actions tab.
14. Click Set Field Value.
15. Select Case Status in the Field drop down.
16. Click the Static Value radio button.
17. Click the button at the end of the Selection field.
18. Click List.
19. Click Closed.
20. Click Save.

Note:  The workflow runs every 30 minutes but users can also set different intervals. Please see Answer Id: 11519.
This is an alternate solution for Enhancement 85364.