If you are in Human Resources (and assuming the employee responding is not from your department), do not divulge the specific information to the department. The employee will feel either embarrassed or as if his/her privacy has been invaded. This can only serve to hasten the person's departure.
Additionally, you do not know the full situation. Maybe he or she was just sending it out on a lark or placing the resume on a recruiting board "just in case". Do, however, use this information as an indication of possible unrest within the department that the employee works for. Keep an eye open to potential problems and review exit interviews of others in this area to gain clues into what might issues employees might be concerned with. It also might be a good time to talk to the Manager or the employees about how things are going in general. No need to bring up the found resume.
If you are a department manager or small company owner and you come across the resume of one of your own employees, you have three choices. You can ignore it, you can bring it to the employee's attention and find out what the situation is or you can talk to the employee or a group of employees about the morale in general. I would opt for the third choice. The resume was NOT meant for your eyes no matter how legitimately it came to you. A general morale check would be more appropriate.
And finally, if it's an employee that you were hoping would leave, (which these things tend to be) thank your lucky stars and re-send the resume to all other companies in your area.
-Beth N. Carvin
Chief Executive Officer, Nobscot Corporation
Carvin teaches classes in Hiring The Best, Ethics In Banking, and Employee
Relations for the American Institute of Banking. She is a member of the Society
For Human Resource Management and the Human Resources Mentoring and Networking