I want to write a proper, thorough reply to this with citations to specific references and mentions in the story, but uh, a tree fell on my house so I've been a bit too busy to do that lmao.
BUT, to give an incomplete answer:
Yes, adventurers get paid for work they do inside of the dungeon, or, they just harvest monsters/plants/treasure that they find. The dungeons are a kind of boom town, similar to a gold or silver rush, which means that the entire local economy is based on people trying to extract wealth from the dungeon, since it's dangerous but easy work, anyone can try to do it with very little resources, and the potential for profit is huge.
Someone with almost no money could, potentially, go into the dungeon and walk away with enough money to start a business, or buy a house or a boat. If they don't die. If they're lucky. Desperate people cling to the hope that they will be one of the lucky ones who become insanely wealthy.
Based on things Kui's told us in the manga and the extra materials, we know:
- You pay a fee or a toll to be allowed to go into the dungeon. Access is controlled by the local government. Some people avoid this, like Senshi and the orcs since they just live in the dungeon and avoid leaving.
- Many people die, give up, or fail to accomplish anything useful in the dungeon. These people probably generate a good, steady income for the island, since they pay fees but don't have to be rewarded. The lure of trying to strike it rich keeps huge hoards of people flowing in steadily. Most money in boom towns is generated by all the people who are trying and failing to get rich buying things from local people (food, supplies, lodging).
- When a dungeon first appears, it is full of easy to harvest gold and treasure. "Gold peeling" is how Laios and Falin started out, and it's literally going into the dungeon and peeling gold off of the walls and statues, and taking any easy to transport treasure with you.
- Various tasks need to be done in the dungeon to keep it safe, clean and accessible, and all of these result in a person either being paid by the lord of the island, or the person who they have saved. Killing dangerous monsters, finding people who have died and taking their corpses to the resurrection office, reporting changes to the dungeon, discovering new paths, etc.
- When gold and treasure that is easy to find starts to run out, people turn primarily to harvesting monsters. They are probably paid a bounty for every monster they can prove they killed (bring back some body part that a monster only has one of, like a tail), and then they can also sell anything else they harvested from the monster in the market (meat, the rest of the hide, horns, teeth, claws.)
- You want the dungeon to stay safe with a well-managed monster population to prevent something like Utaya from happening.
- But if you kill too many monsters, now that the treasure is gone, there won't be any profit reason for people to go into the dungeon anymore, and your economy will collapse.
- So you need to manage the dungeon and keep the monster population high, but not too high. This is what the Shadow Lord was complaining about. He thinks that if they evacuate the dungeon the expensive monsters they are currently harvesting may stop manifesting/spawning/being born, and all that will be left to harvest is mushrooms and slimes, which are not worth a lot of money.
Laios' group had an assignment from the island lord to try and find the giant doors on the 6th floor that nobody had been able to get past. That was what they were trying to do when they ran into the red dragon and Falin got eaten!
Despite everything, at that time Laios' party was the number one team on the island, capable of going the deepest into the dungeon.
Kabru's team is also considered pretty good, despite how often we see them dying - this should tell you how bad many of the teams that go in are! Most of them don't accomplish much or anything... Just like a boom town, where most miners go into debt trying to find gold, and only a few strike it rich.
This is what Rin is talking about in her first appearance, when she scolds Kabru for being too modest around other adventurers. She wants those other people to know that they are not going into the dungeon for profit and that they're not like the rest of them, dream-chasing fools hoping to make a payday.
She's offended anyone would mistake them for people like that, meanwhile Kabru would rather keep their motivations obscure and not advertise that they're in the dungeon on a moral crusade, not a financial one.
It should also be noted that the dungeon has a lot of criminal activity going on inside of it, because it's not well monitored and it's easy to conceal your activities. There's also a population of people who can "no longer live on the surface" for various reasons, such as being wanted criminals, exiles hiding to avoid vigilante justice, people too poor to leave because they wasted all their money trying to get rich and now they can't afford to live on the surface, or leave the island.
Essentially there is a population of homeless people living in the dungeon, eating anything they can scavenge, begging and stealing to stay alive. This could even be part of the taboo on eating monsters in the dungeon - that's something poor and desperate people do, and doing it is seen as a sign of how low Laios' party has fallen.
This is also why Kabru is so worried about the Touden party: their financials are a mess, but they keep going into the dungeon. Why? People think they are good, but maybe they're secretly criminals? Are they on the run from the law? Kabru has no idea, since "they just really love monsters and this is fun" is not a motivation ANYONE ELSE ON EARTH HAS.
The Toudens can't even say "we're monster researchers trying to write a book on monsters." They're just hobbyists, they just like them a lot. Kui tells us that Laios was encouraged to become a monster researcher but the studying was too intense for him.
It would be like finding out someone who works in a coal mine that kills 80% of the miners doesn't actually care about being paid, they just loooove coal and want to be around coal all the time.