Not many people use portable radios operated with a 9v battery anymore, so they tend not to have the more informative experiences that a continuous audio signal can provide. I had my great learning about carbon-zinc batteries when I was laid up in bed with mononucleosis in 1966, and had to rely on the near-dead batteries in my radio to be able to hear my favourite tunes on the top 40 playlist. I'd leave my radio off for 90 minutes or so, to be certain I had enough juice regained in them to hear the tunes I knew would be played at relatively predictable times (and at the time, I was enamored of the guitar intro to The Hollies' "Look Through Any Window:)
Carbon-zinc will spontaneously "recharge" if you leave them for a bit. That is, the chemical reaction will reverse with disuse, and they will regain a little bit of life. And I emphasize the word "little". If I kept the volume down, I could hear a whole tune, but if I cranked it up, i'd get a very audible compression, until finally the batteries crapped out. This "Hold on, give me a sec to catch my breath" phenomenon would only occur when the batteries had dropped in voltage a bit.
The "dying battery effect" is NOT, as some would have it, merely a lower, but stable, voltage. You won't get it from an alkaline, or lithium-ion, or from a wallwart with a bunch of diodes in series, or anything similar, because they are providing a power source that can meet the current demands of the pedal. What is fundamental to the impact a dying battery has on a fuzz (and nobody seeks dying battery sounds for delays, tremolos, EQ, wahs, etc.), is that a brief respite allows the battery to catch its breath but a peak transient saps the battery of current. That is, the impact of a dying battery on a fuzz is a dynamic phenomenon, that corresponds to picking strength, and input signal amplitude. That's what imparts a certain sponginess or compression, in addition to a bit of gateyness here and there.
I'm confident something can simulate that, but I'm equally confident that much of what gets suggested as a dying battery simulator probably won't, simply because they do not incorporate any means for the power source to "choke", cough, wheeze, or whatever you want to call it. That is, they provide a steady and stable current delivery capability.