It takes courage to admit that you resigned from your previous job because you were faced with being fired. But honesty really is the best policy when you're completing employment applications. You'll only make it more difficult to find employment if you try to withhold information from potential employers, so don't try to conceal the true reason for your resignation. Employers know that you're not the first person to resign instead of getting fired, and you won't be the last.
Few job applications even have enough room to give details about why you left your previous job, so you might only be able to insert "resigned" in that field on your employment application. You needn't try to cram into such a small space the details about your resignation if all that fits is one word. Provide succinct information on your application -- you will have plenty of time to elaborate during your interview.
Some job applications ask questions such as, "Have you ever been terminated from a job?" or "Have you ever been asked to resign from a job in lieu of being fired?" If you encounter the latter, you'll have to admit that you have been asked to resign in lieu of termination. But if the application asks only if you have been terminated, you can truthfully insert "no" as your answer to the first question.
Your resume is a marketing piece that illustrates why you're the best candidate for the job. Therefore, its focus is on showcasing your talents and skills -- not recounting the reasons why you left previous jobs. There's no reason why your resume should contain the reasons why you left any of your previous jobs, regardless of whether you left to pursue an amazing career opportunity or because the business closed down. On the other hand, if you list several short-term jobs on your resume, a recruiter or hiring manager could ask you to explain the reasons why you left those jobs.
Present your qualifications from a positive perspective, whether you're completing a formal job application, describing your work history on a resume or talking to the interviewer. When a potential employer asks why you resigned, say that you were given the opportunity to resign instead of being terminated. Explain the reason, especially if it casts a favorable light on your work ethic. For example, if your previous employer acknowledged your conscientious effort at performing your job duties, but the job just wasn't suited to your skill set, give details about your effort and the ultimate outcome. If your resignation in-lieu-of termination resulted from a policy violation or willful neglect of your job duties, explain what you took away from the experience and your improvements.
If you're unsure how your previous employers will characterize your resignation, call them before you embark upon your job search. Confirm what your employment records show and indicate the type of separation that you're providing to potential employers. This ensures that you're providing information that's consistent with your previous employer's records and that the information you provide can be verified during background checks or employment verification.