I am being a little generous with my nomenclature. This slush fund acts as a second-tier emergency fund and has existed going back to my early working days. My first-tier EF is a small cushion in my local bank's checking account I tap into to cover smaller, unforeseen (but more common) expenses. This larger second-tier EF is used to cover larger, unforeseen (but less common) expenses the first-tier EF can't cover. That's its purpose.
So, this slush fund is a holdover from my working days, but smaller than it was in my working days because it is an intermediate-term muni bond fund. When I was working, and my income in a higher tax bracket (and the tax brackets were higher in the 1990s and 2000s than they are today), it paid to have my bond allocation in muni bonds.
In 2008, before I ERed, I had about 50% of my AA in muni bonds. In the first few years of my ER, I made a concerted effort to reduce my muni bond holdings because my marginal tax bracket went down a lot. Instead, I directly and indirectly transferred funds into a taxable bond fund. My muni bond holding dropped to about 9%, with the new balance reduced to my comfortable but relatively minimal "slush fund" amount (around $45k).
This bond fund also has checkwriting privileges, something you don't find much outside of money market accounts these days. This provides added liquidity and easier access than having to transfer money from a mutual fund account to my local bank first, then write a check. And this fund earns about 2-2.5% annual, mostly tax-free income per year, with some but not a big risk to principal. I have written 18 checks in the 26 years I have been in this fund, so I rarely need to withdraw from it, and I have basically broken even on them overall.
Does that help?