If another player takes your loot in a "your map your loot" party (also known by owner needs/others greed), they will be allowed to keep the item and you *will not* be reimbursed. Chances are they also face no consequences- no suspension or ban.
TL;DR: If another player steals loot from your map in one of these parties, you will not get it back and you're just SOL. Be careful.
In my case, I was running with a random group in PF on Famfrit- something very common, at least here on Primal. The party finder listed the rule: Map owner needs/other players greed. Very clear loot rules. When we got to my map, I happened to get two frontier cloth drops (the latest map material- was going for 1.64mil at that time) on which one of the other players rolled need on. He managed to win one of them. I asked him to give it back to me when the map finished, and he said "oops." Sure, it happens; muscle memory has caused me to hit need a few times when I wasn't supposed to, and I promptly traded it back afterwards. But after we got out, I sent a trade request, which was immediately declined. Sure, maybe he was doing something. Sent another. He gets a Disconnecting symbol.
Note: prior to my map, he went afk for around 15 minutes, getting carried through a Lyhe Ghiah portal and a few overworld maps. He suddenly came back when we couldn't move on due to him not rolling on loot and I asked if we should kick him. This was right before my map.
I reported him, and also got told that GMs cannot replace the item. I'll admit, having had an awful week and being incredibly annoyed over this, I have checked to see if any suspension or ban occurred- he has been happily doing whatever in the firmament ever since. (It's been well over a day since I was contacted by a game master)
I asked around a bit on discord, and this is not an isolated event. You're pretty much SOL if this happens to you, unless someone in your party feels bad enough to give one to you or something.
I'm sure others have seen the absolutely absurd reasons people get suspended or banned in this game lately- anything from spamming holy in city-states (admittedly annoying, but just as much of harassment as stealing loot from someone's map!) or even advertising an RP venue in the party finder.
So why are people allowed to steal materials from another person's map, where the loot rules were clearly defined as the owner of the map is the only one who is allowed to roll need (loot rules in which they agree to by joining the party finder), keep it, and basically just get away with it?
I was debating whether or not to post this as it may plant the idea in other's heads that they can get away with this, but I really hope this shows people the danger of running these loot rules, and maybe motivates people to finally do something about this.
Edit for clarity: The purpose of this post is primarily to warn others of the dangers of running these loot rules with randoms; you will lose these materials and never get them back. Please be careful.