Agree wholeheartedly. Filing a claim for unemployment insurance benefits should be your first action, regardless of your reason for termination. The decision to grant benefits will be made by the agency after speaking both with you and the employer, and it should, in any case, give you a very good idea of how the former employer is interpreting your termination for cause.
By the way, the whole "we will give out only your dates of employment and reason you left the job" is totally not binding in the whole unemployment system (which is, for most all intents and purposes a closed system, in that no other employer or outside entity will be able to read or see what the employer has said during the claims approval/denial process.) They will ask, and the employer is fully entitled to respond with what they terminated you for, a determination will be made by the unemployment system whether their reason meets the definition of job related misconduct sufficient to justify termination.
If the issue with your whole question is related to unemployment insurance approval, let us know that, and we'll address it. Essentially, it's a whole other ball of wax, and yes, in that agency situation, they are NOT obligated or committed to staying on a script of providing dates of employment only.
But what goes on in unemployment insurance has nothing to do with your moving forward and obtaining another job. Unemployment benefits, even if approved, are designed to be a very temporary situation, until you move forward into another position. And I do agree, lying to a prospective new employer is rarely a good idea.
However, you can work on your responses before you are asked, determine just how much basically truthful information it is necessary for you to provide in an interview situation to a potential new employer. If you worked somewhere for say, five years, and you were terminated for cause, it would be to your advantage to emphasize the job responsibilities and the things you did achieve positively during those five years, skills you acquired, successes you had, much more than camping on how you were mistreated or falsely accused at the end of your employment. Except for when you are filing a claim for unemployment, no one now wants to hear very much more about what a terrible job that was, how awful the supervision or the situation was, or how badly you were mistreated.
I would, in interviewing for other jobs, work under the assumption that what they were going to get from a past employer was just that, the confirmation that you did work for them and your dates of employment. It is usually up to you what you say about what went on at that job, and you can usually find ways to make it sound extremely positive, even if it wasn't so nice.
The problem is that people who are coming out of a bad job situation, especially those who have been, for perhaps the first time in their job history, terminated for what they feel is an unjust reason, or "for cause" are overly involved in this situation which has been all important to them for the past however long. They will tend to feel that what has happened to them, the termination for cause, will forever be a factor in their lives. This isn't necessarily true.
"Left for more opportunities" "left to find better job" "wished to change field of employment" all will work as a brief reason for leaving. My experience has involved people who, in the name of being strictly honest, have written on job applications things like, 'fired for cause, accused of stealing' and 'manslaughter' (figure that one out!) and my personal favorite, 'recaptured, returned to prison.'
