Thank you for the information and your question. Unfortunately, unless you have a contract or company policy that provides you more protection, not only could your employer let you go for any, or no, reason and no notice, but they can also let you go for cause for "no call, no show." No call, no show is considered to have occurred anytime an employee is not at work when they are scheduled, regardless of the reason. Whether your last incident was job abandonment I can't say, but it could still be considered cause if you didn't show to work or call.
If you did call and had permission not to come in then it wouldn't be "no call, no show" or job abandonment. In this situation, the only other exception to your employer's right to let you go, with or without cause, is that they can't target you for different treatment from other employees who have done the same thing merely because of your sex, race, national origin, age (over 40), religion, disability, pregnancy, or AIDS/hiv status.
So, if one of the exceptions does apply in your case, you should sit down with a local employment law
attorney and discuss your case. If not, then the termination
would have been lawful. That said, you can still file for UI benefits and although your employer will likely dispute
your eligibility, you can appeal a denial and then your employer will have to prove that you did what they said (abandoned your job). If the hearing officer sides with you, then you can received UI benefits.
Just keep in mind that qualifying for UI benefits has nothing to do with whether or not you were lawfully terminated. It is a totally different set of laws.
Please feel free to ask for clarification. I would be glad to assist you further if I can.