The 6 month emergency fund is good for another reason, as f-you fund: in case working conditions get bad, you know you can just walk away. Somehow the knowing is enough, you never have to mention it, the confidence somehow shines through if you have a difficult chat with your manager.
Lol it's not that big a deal if you lose a job when you have around 12months living expenses saved up. So that goes twords living expenses, then you get unemployment at 60% of income. People need to move on, and stop being so emotionally invested in their work.
You are most likely an at-will employee. You or the employer can terminate the relationship immediately giving any reason or no reason. Just have money saved up and don't be afraid to quit without notice to something better if you need to.
The big lesson I try to pass on to everyone. Don't ever assume you will have a job next week. Be polite to any headhunters, assuming they are the professional kind, keep your resume up to date, network like crazy, have a few side project plans, don't be afraid of small jobs on the side, and most importantly keep a 3 - 6 month emergency fund. That fund doesn't have to be what you make in 6 months, but at least what your bare bones expenses are (mortgage, utility bills, minimum credit card payments), and try to keep your have-to recurring monthly expenses lower (mortgage / car payments, etc). That doesn't mean you can't spend on extra stuff, just make sure you can cancel them at any time.