How to get unpublished date of a node?
Create a View (using the Views module) that shows Content and displays a Grid of fields in Display format. Add the field Updated datein the list of Fields. Be sure to select Published: No in the Filter Criteria. You can add other fields if you want (e.g. Title). This will get you the date of the last update. If the node is not edited after being unpublished, the unpublished date will be the last update.

EDIT:
If you specifically want to show the unpublished date, I am not aware of a module for this. I suggest another approach that is a bit circuitous, but it works. It involves creating a date field to store the unpublished date, and using Rules to set it when the node is unpublished.  


Download the following modules: Date and Rules. 
Edit your Content Type. Create a date field
Create a Rule that reacts to After updating existing content of type XX. Add a condition node:status equals unpublished
The Action should be set the date field value to now


That's it. Now, if you want to hide the date field in the node edit form or display, you can play around with your theme's CSS classes or explore other modules. Let me know if you have questions