I'm an engineering graduate looking for job opportunities while at the same time I'm on a internship in a big company. Recently, I received an offer of full-time job with higher pay than currently. Motivated by raise in salary, I accepted the offer and gave a notice to my employer. I did not receive any written offer: In country where I live, there is no possibility of signing a contract before giving a notice. There is something called "letter of intent" which can be used as legal just-in-case document but no employer bothers with it for entry-level jobs.
Fast forward to the last day of my job, I received a call from the recruiter that they need to change the offer to lower salary, which is well below what was proposed before and almost exactly how much I'm paid on my internship.
With this information, I'm really stuck on what to do. Firstly, this behaviour looks to me as a extremely bad sign on my soon-to-be employer. Secondly, if I knew about the final offer in advance, I probably would never have given a notice in my current job.
If I choose to keep the new job, how can I go about negotiating back toward the original offer? If I refuse the new job, what options should I be aware of?