Change happens. Just when a department is fully staffed with trained people and everyone has a fresh supply of business cards, someone will submit a letter of resignation. In an ideal world, every associate who resigns will provide her employer with a two-week notice, which is an unwritten rule in the world of business. Two weeks doesn't give an employer enough time to hire and train a replacement, but it can still help with the transition.
An unhappy or hostile employee may quit with just a moment's notice. Don't let such a hasty exit negate the usual practice of getting a letter of resignation. Ask for something in writing stating that the employee is resigning from their position. If you receive no cooperation and there is no witness to the verbal resignation, call a witness into the room. This is to protect the company from an employee who may claim that she was the victim of a wrongful termination or who wants to file a claim for wages through unemployment insurance.
The witness should be a manager or other exempt-status employee. In the presence of the resigning employee and your witness, indicate the employee's intentions, and that your request for a letter of resignation has been denied. Record the conversation in writing, then sign the document in the presence of the employee (if she is still in the room) and ask your witness to do the same. It is unlikely that the departing employee will sign the document, but the signature and attendance of your witness is sufficient backup for your files.
If an employee quits and refuses to give you a letter of resignation, call someone into the room (preferably another manager) to witness that the employee has resigned. Get a statement in writing from the witness about the verbal resignation. Proper documentation of a resignation is important and worth this step when necessary.
When an employee who is an asset to the company resigns, you won't want to see them leave, especially if they are going to work at another company. They probably feel that the new job is a better opportunity for them or it may be a career change into something that they really want to do. Wish them well and work with them to finish up projects that are still pending, and train coworkers to take over job duties until a replacement is hired. It is in everyone's best interest that the employee leaves on good terms.