What if the person only has tax deferred retirement accounts and would take a big penalty if cashed in? "Emergency"
So, there was that whole discussion of ROTHs and withdrawal technicalities, but another answer is just: ok, so you pay the penalty. This is only an issue in an actual emergency. Actual emergencies are rare. You can't predict the future, and therefor you want to have some option available to cover that rare chance, but it doesn't make sense to take a known and continuous financial penalty to avoid a possible one time financial penalty.
Lets say that for whatever reason, a tax-deferred account works out better for you.
You can either put 10,000 in a savings account as a EF, and lose out on 5% a year in potential interest for ever, or you can put it all into the traditional IRA, and when/IF an emergency comes up, you pay a 10% penalty.
In just 2 years in the IRA, the account has earned as much as the early withdrawal penalty would be! Which means once you go 3 years without a 10k emergency, you are losing money by having the large EF, even if you do have an emergency and have to pay the penalty.
But wait! There's more!!
The penalty is waived for actual emergencies!!!
You were unemployed and paid for health insurance premiums, or permanently or totally disabled, or paid for medical expenses exceeding 7.5% of your adjusted gross income. Its also waived for college expenses and buying a first home, and those aren't even emergencies.
Basically, having a liquid EF which could be invested is gambling that a crises WILL occur, and will occur soon, (and repeatedly, if you maintain it post-crises) which statistically doesn't make sense.