Yup, Typically they walk in a large circle, worst cases they cross over spawning areas of mobs. Ive seen max level ones that are in starting zones before. Imagine being lvl 10 and killing mobs for a quest and a max lvl raid boss just walks through there spawn zone, agroing do to proximity and slaughtering you. Or image again in a starting zone killing mobs and among them is a slightly larger version of them, its name is different sure but that only visible once you click on it. And that slightly bigger one is 10 times the level of the others a a raid boss, or to be clear in this case a world boss. Actually both im talking about were world bosses, which is way worse than raid ones, raid ones are for a set number to fight, world ones are for a server to fight at once.

“Is a “wandering raid boss” a thing in some MMOs?”

A moving or randomly appearing mini boss is completly normal in many games. For example FFXIV has FATEs, that pop up on the non instanced maps and if you walk into its area and your level matches, you get auto joined. (For high level players, you have to manually lower your level to join.) These FATEs could be as simple as an area defense mission with NPC assitance (usually from the guards in the area) with many small standard mobs or a single larger boss mob or several waves of progressively stronger mobs with a mini boss at the end. FATE enemies are always marked in the hud, so you could actually tell them apart from the normal wildlife. If a player gets caught in a FATE and the player is quick enough, it’s usually possible to run away in time as the mobs don’t pursue players outside the FATE’s area, which is also marked on the map. The only case where it’s annoying is when a quest battle is in progress and a FATE spawns in at the same area, so a solo player has to fight with the original quest npcs and boss and the FATE’s npcs/boss and any wildlife that gets pulled in with an AOE or multi target attack. It’s alway a good idea to lean out the wildlife and check for FATEs and their schedule in the area before activating a harder quest location. Also a pro tip is to check the enemies level before engaging. NPCs and mobs with ?? in place of their level marker are usually non killable by the player at their current level or require certain quest items to make them fightable.

So generally if you look around and don’t start hittin everything that comes across you, then it’s mostly safe to run around on the open maps. Also if you get aggro from anything, there is a marker, so you can usually run away before a pop up mini boss kills you in one or two hits.

ps: btw. catgirls are a playable race in FFXIV and also make up a large portion of the NPCs and some percent of the mobs…