I'm not sure if you saw my questions. I'm going to address your question to the extent that I can without the information I requested, but taking into consideration all the facts that you did include.
In employment law, unless you have a contract of employment that expressly states that you can only be terminated for cause, you can legally be terminated at any time. This is called "at will" employment and is recognized as the default employment status in your state.
This is important for understanding if the employer here could legally let you go. Without a contract, they could, so your facts don't really change the issue of "at will" employment. You didn't have to quit for your no longer working there to be legal. The employer could terminate too "at will" and that would be legal.
So, the only way then for their decision to release you to be illegal is if you can state that their decision was really based on discrimination due to your race, religion, gender, age, disability or FMLA use. You've not made any mention of any suspected discrimination. If you do feel that it contributed or could have, you need to file a complaint with the Equal Employment Opportunity Commission in your state to have them investigate the basis for letting you go more closely.
Finally, we need to address unemployment. If you decided to stay with the former employer because they told you that was possible, and you only turned down another position because it was possible, then you can file for unemployment.
If you turned down the new employer outright, not having any idea if you could stay with the original employer, then that can be seen as refusing gainful employment which would be a disqualifier for unemployment.
Your facts suggest that you were at least led to believe that could stay with the old employer and didn't realize you weren't until they made the decision to tell you that were no longer with them (a termination). On those facts, it would be reasonable to apply for an argue for unemployment.
If you have any further questions, please let me know. I invite follow up questions, so use REPLY for those. If you have no further questions then good luck going forward and please do not forget to rate my service with a top-three rating so that I receive credit for working with you today. Also, feel free to request me in the future, if you have question concerning a different matter.