I had the idea of the blanket Pokemon in my head since you posted the prompt, and I just finished with establishing it:
Fairy | Ground
Base stats: 500
Appearance & description:
Basically is sentient blanket, and behaves as if someone or something was under a blanket at all times, like the typical ghosts. However, this is not a ghost that only lurks in the dark, as it can be found on open fields and in daylight, showing that is more of a Fairy Pokemon than a Ghost one. It has 2 dark spots as eyes. A peculiarity of it is that it only moves around while it is on a surface: if one were to lift or hang the blanket, it becomes mostly immobile and nothing is found underneath, except for some signs of digging on the spot, and it will become active again once the the blanket makes contacts with the ground again. However, if the blanket is left hanging for too long, it will eventually struggle and try to drag istelf into any available surface, revealing that the blanket itself is the Pokemon. Another trait is that the blanket is incredibly soft, inviting Pokemon to approach and fall asleep or rest over it, something it has no problems with and actually it seems to enjoy the company. Like Vivillon, is has different patterns depending on the world location, some having classic patterns like a white and red stripes picnic blanket.
Soothing - 30% if causing sleep when hit by a contact move
Sweet Dreams - If the Pokemon and/or its allies are under Sleep status, they recover 1/8 of their max HP every turn, also their Sp.Def is doubled.
Notable & flavor moves:
Basically a combination of Yawn + Block. It entraps the Pokemon and induces Sleep status at the end of the next turn.
Support and wall. It may not have too many resistances, but 2 immunities are welcomed. Also the Ground type should scare Steel, Poison and Fire Pokemon that threat it. With balanced defenses overall, it can be built both for Def and Sp.Def, and comes with 2 abilities to support either. Fluffy for Def is straightforward, while the Sweet Dreams ability is more tricky to use, fit better for Rest builds and a bit intended for double/triple/etc. battles. Depending on the setup move of choice, Bulk Up or Calm Mind, it can enhance its Atk or Sp.Atk to better scare those Steels, Fires and Poisons, or even get a shot at sweeping. Alternatively, it dedicate to support and disruption with Spikes, Screens, Lovely Kiss and its introduced move.
A Pokemon with an ability that activates one of the underused field-based moves that last 4+ turns when it is switched in. For example, Mud Sport, Water Sport, Wonder Room, Magic Room, Gravity. Avoid Trick Room, Sticky Web, Spikes, Stealth Rock, Tailwind, the Terrains.