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It isn't. We can find soft iron core in transformers and electric magnets where word stator is meaningless.
Stator is the non-moving part around (see NOTE1) the rotating part (=rotor) in an electric motor or generator. Actually stator contains only those non-moving windings and their iron core which interact magnetically with the rotor. Stator and rotor often have soft iron core for magnetic effectiveness, the flux will be stronger and better placed with it. But soft iron core isn't a must.
Stator hasn't always windings, many small motors are made with permanent magnets in stator. Soft iron can still be used to direct the magnetic flux better.
BTW. Soft iron core is common also in knives, often there's hard steel only on the surface.
NOTE1: There's a comment which says that stator isn't allways around the rotor. That's true.Nothing prevents having the rotor as an outer ring around the non-rotating stator. More: there exists rotating electric machines where the rotor and stator aren't coaxial. An example: The unipolar motor which was common in kWh-meters before modern remote readable electronic meters.
Historically remarkable invention was Hippolyte Pixii's generator (about. 1832), where stator and rotor were coaxial, but they were face to face, neither was inside the other:
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