Once you have more than about two years worth of salary invested in a brokerage account, you don't need a cash emergency fund anymore. You can withdraw cash from a brokerage account instantly, up to a large percentage of your total balance, without selling anything.

This creates a margin loan, and then at your leisure you can sell your investments to pay the loan, only paying a few days worth of interest at most. Or you can keep the loan. The rates are far better than credit cards and there's no minimum payment or required repayment schedule. Interactive Brokers' current margin rate is 1.57%!