Can they do that?

What is the name of your state?
Oregon. I worked for a major retail company. I was pulled into the office one day to get fired. They were going over scheduling issues with me, saying I wasn't working any scheduled shifts, that I had been switching shifts to often with other coworkers(even though they were all aproved by my supervisors). Anyway they told me they were to terminate my relationship with the company because of this. I had never been counseled or nothing was ever documented in the past that this was a ongoing problem with me. I left the building and came home realizing that I hadn't signed a termination paper. The only thing that I had signed was a pay out for that week. I later called for a copy of my file and went in to pick it up. One of the managers sat me down and had me tell her everything that happened. She was asking me crazy questions like was I getting a attorney. I later read my file and in it was a termination paper, that didn't have my signature on it but my name was printed in its place. The reason now for termination was poor performance. I had no written documents in my file of poor performance, in fact the only written document that was neg. was that I didn't have my back belt on one day. Is this all legal? I had been a supervisor for 4 years at this company, shouldn't they have counseled me or even demmoted me before terminating me?

As an "at will" employee (as the vast majority of us are), you can be terminated for any reason or no reason, just not a specifically prohibited reason (i.e. BECAUSE of your age, race, gender, national origin, religion, handicap, etc.) Nor is it necessary for the company to have you sign any termination documents.

So yes, they can do this.