I am currently building my emergency fund. My contingency plan needs to cover not only events like "job loss" but also "North Korean nukes / I need to get out of here immediately", so it's a little different from most people. I aim for 6 months of living expenses + relocation money for 2 people and a dog. I am confident that in a country with no visa requirements (ie in the EU), either myself or my partner could find a high paying job within 6 months, even in this economy.
In practical details, it means having about 1,500+ euros of perfectly liquid savings in my country of residence, another 1,500 in my country of citizenship, and 7,000 in an easily accessible hub with good banking protection (not implemented yet, but I'll probably go for Singapore as it's a cheap place to fly to from anywhere in the world).
At the moment, I have the 10,000 aside but they're all in one place (earning a guaranteed 3% a year, which is less than the market, but a price I am perfectly happy to pay in exchange for liquidity).
I have more mid-to-long savings and investments for other purposes of course, but they're not as liquid and I may not have a chance to access them if I had to leave the country with days or hours of notice.