What would happen if dead leaves suddenly became the most valuable currency in the world?

Well for starters, at least one famous economist would be discredited.

A meme saying "Could Autumn leaves soon be worth more than gold?" at the top, followed by pictures of leaves and a gold bar. At the bottom is a caption saying "A famous economist says 'what the ****? No, why would they be?'"

People would start killing trees for the dead leaves.
Unfortunately I don't think I'm even being cynical.

We will trees for lumber. This isn't cynical at all.

Edit: idk if I meant kill trees or will cut trees lol.
- No, you'll trees.
- You don't need to axe murder the tree to get leaves. I expect it to be more economically sustainable to keep your tree alive.
  
  Lumber is the body, so not killing the tree is kinda off the table.
Alas, I don't think that's being cynical at all. Or maybe I'm, too?

Immediate inflation is what would happen.

It would have a devastating effect on the eco system, since many flora and fauna depend on those leaves (for shelter, to feed on, to hunt in, to lay eggs on), and many more flora and fauna depend on those that depend on the leaves, and capitalism doesn't give a fuck so the leaves would promptly be removed from the environment by one corporation or another so that they can profit, and we'd be fucked even further.

In short time the only trees allowed would be on corporate property. They would grow rows of one type of gmo trees with maximized leaf growing ability. They would use leaves to pay wage slaves to harvest leaves.
- They would use leaves to pay wage slaves to harvest leaves.
  
  Wage Slave: Please sir, my family is starving.
  
  Corpo: Silence! You know the punishment for theft.
  
  Wage Slave: But sir! In a single 14 hour shift, me and my coworkers bring in an average of 1.2 tons of dead leaves a day. It costs but a handful of leaves to feed my children, and a small paper bag to house them.
  
  Corpo: Ah, so you know of your costs, yes. But you think not of the costs for those who would pay you. My costs are numerous, and if I am to pay you, and pay still more of your coworkers, they must first be met, and met in full.
  
  WS: You are right, sir, of course. Forgive me, for I know not the burdens beared by those cursed with fortune.
  
  C: Then allow me to educate you! Your coworkers and you bring to me 1.2 tons of leaves everyday. Every day! Do you know the cost of storing 1.2 tons of leaves?
  
  WS: I have never had the leaves necessary to warrant storage, sir. What a burden this must be.
  
  C: A burden, yes! And what's more! If I am to leave my leaves unattended, who is to say the likes of you won't come in the night to take what I have rightfully earned?
  
  WS: Another thought a stranger to me, sir, for I have naught the possessions to fear theft, save for which I have thusly stolen from you.
  
  C: Indeed! And lucky you should feel to be worry free of thievery! And finally. Why is it, do you think, that not everyone grows their own trees, farms their own leaves?
  
  WS: This I do know, sir! This is the law of the land!
  
  C: The law of the land, precisely. But the law does not avail itself cheaply to those who have; nay, for those burdened with the curse of fortune, justice is bought, and bought with deep pockets. For the cost of justice far exceeds the cost of storage, the cost of vigilance, even the cost of labor (which, as a laborer yourself, I need not remind you is exorbitantly high!).
  
  WS: I have never thought to purchase a law before.
  
  C: And it is my wish that you never shall. Great are the troubles of those forced into my position. This is why you must toil, why the days must grow longer and the suppers fewer and further in between, why those who have must always have, and those who don't must never receive; lest you be faced with the ugly wrath of capitalism.
  
  WS: Capitalism! Gods, anything but that!
  
  C: So you see now, Wage Slave, why you must accept this punishment for reaching out to the forbidden fruit.
  
  WS: Please, sir, a decade of unpaid labor is but a gift to someone like me, who was but this close to falling into the clutches of prosperity!
  
  C: Go, then, and sow for me now what I shall later have you reap.
  
  WS: May I sow the same field you have my children working?
  
  C: No.
  
  WS: Thank you!

“Thank you. Since we decided a few weeks ago to adopt the leaf as legal tender, we have, of course, all become immensely rich.”

Ford stared in disbelief at the crowd who were murmuring appreciatively at this and greedily fingering the wads of leaves with which their track suits were stuffed.

“But we have also,” continued the management consultant, “run into a small inflation problem on account of the high level of leaf availability, which means that, I gather, the current going rate has something like three deciduous forests buying one ship’s peanut."

Murmurs of alarm came from the crowd. The management consultant waved them down. “So in order to obviate this problem,” he continued, “and effectively revalue the leaf, we are about to embark on a massive defoliation campaign, and. . .er, burn down all the forests. I think you'll all agree that's a sensible move under the circumstances."

The crowd seemed a little uncertain about this for a second or two until someone pointed out how much this would increase the value of the leaves in their pockets whereupon they let out whoops of delight and gave the management consultant a standing ovation. The accountants among them looked forward to a profitable autumn aloft and it got an appreciative round from the crowd.”

― Douglas Adams, The Restaurant at the End of the Universe

I literally don't know if you made this up or if it's actually from a book.

Either way... Well done
- It's from hitchhikers guide to the galaxy

That is a minor plot point in The Restaurant at The End of The Universe by Douglas Adams.

They propose & implement a defoilage campaign to combat inflation.

It has already happened

Tea bricks were the preferred form of currency over metallic coins for the nomads of Mongolia and Siberia. The tea could not only be used as money and eaten as food in times of hunger but also brewed as allegedly beneficial medicine for treating coughs and colds. Until World War II, tea bricks were still used as a form of edible currency in Siberia

Money can be anything.

https://en.wikipedia.org/wiki/Rai_stones https://en.wikipedia.org/wiki/Tulip_mania

Then money really would grow on trees.

Time to burn down some forests to save the economy and start a job as a telephone disinfectant

I would be rich as fuck

Trees would lose all their leaves as people pick them off and let them die in a bag somewhere

I’d wish you a good harvest this fall!

I’d finally clean my gutters.

Maybe next weekend….

People would start cutting down trees and plants so they could have more. Then that would cause inflation which in turn would cause people to cut more trees and plants. Carbon dioxide would soar, and then we all die.

So, nothing changes, got it.

People who were already poor would remain so. Most people who aren’t wealthy can’t afford to own acres of land that doesn’t produce crops. If leaves suddenly became money, that would not change the fundamental needs people have of food and shelter. So you’d have the wealthy with vast swathes of forest that would slowly die as they carted out a lot of compost for use in markets, and people who live in apartments or other rental situations would never see a leaf on the ground again. You might see suburban homeowners get really good about caring for their trees and planting more, so that’s one possible benefit but overall this would be a nightmare.