Yes. You can ask the employee to sign a release -- an agreement not to sue you for being fired -- in exchange for certain benefits. Some employers routinely ask employees to sign a release as a condition of receiving a severance package.
If you decide to seek a release from a departing employee, you will probably need the help of a lawyer. In some states, a release must contain specific language or a court will not honor it. And you will want to tailor the release to meet the needs of your company and the particulars of the employment situation.
For more information on releases, see Nolo's article Using Severance Agreements to Avoid Lawsuits.
For a complete guide to your legal rights and responsibilities as an employer, get The Employer's Legal Handbook: Manage Your Employees & Workplace Effectively, by Fred Steingold (Nolo).