If they went through the proper firing policy then technically no. If they did not go through the proper termination process then you need to file a union grievance asap. It's amazing the b.s. work ethics I've seen people get away with and still keep your job. Most jobs without union they can fire you for just cause at any time. With the union it takes literally 1-2 years to fire someone unless they find immediate cause. Even then you can generally fight it. Things fire able  on the spot: Selling age restricted items to minors. Trying to stop customer theft. Stealing merchandise or till money. Violation of policies and procedures to the point of three write ups. In time a lot of little b.s. can get you fired but it needs to be repetitious enough to be a large enough concern.

You can go apply for another store associated with the union and still keep seniority. I've seen a lot of coworkers. Just go to ufcw and see what companies they are affiliated with. If you got fired from say Fred Meyer you can go apply at Safeway or even Macy's and still keep most of your union perks. If you get fired At Fred Meyer you are not an eligible candidate for rehire.