PokéBase - Pokémon Q&A
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I’m not sure if there’s a type combo that can do this. If there was one, it would have to have zero resistances or immunities in regular battles. Most of the answers will probably be Pokémon with one resistance and abilities that make them immune to the type they resist, such as a Pokémon that only resists Electric and sometimes has Lightning Rod. Assuming ability-based immunities aren’t inverted (correct me if I’m wrong), these Pokémon would be immune to their weakness in Inverse Battles.

If you answer, please list every correct answer (but you don’t have to list any Pokémon you can’t get in the games with Inverse Battles unless you want to).

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I checked this link, https://pokemondb.net/type/dual and found there was no dual types with no resistances or immunities.
yea, there arent any. I did find some with only one weakness: Pure Normal types (weak to Ghost), pure Ice types (weak to itself), Water Absorb Lapras (quad weak to Ice), Psychic/Dark types (weak to Psychic)
There are also a couple that don't exist in cart but have 1 weakness: Grass/Rock types with Lightning Rod/Motor Drive/Volt Absorb (weak to Normal) and Ice/Ground types with Lightning Rod/etc (weak to Poison).

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NO

As said in the comments above, no, there are not any Pokemon who's typings have the capability to do this. In other words, no Pokemon has no resistances or immunities, (which is what is needed for this to be the case)nor will there ever be a Pokemon like this(unless a new type is created, or, for some reason, typing's resistances and immunities change.)
Source: The Comments, and looking through the dual type chart myself to double check, using this link: https://pokemondb.net/type/dual

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There is now! Any pure Ice Type only has one weakness: Ice, and abilities are unaffected by Inverse. Therefore, Cetitan with Thick Fat technically has no weakness in Inverse Battles. (but ice moves can still activate Weakness Policy)

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