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We propose a theoretical-clinical framework (developmental and systemic) centered on the theories of enaction and intersubjectivity, and an individualized, contextualized approach to the cognition of autistic adults with profound intellectual disabilities who live in institutions and do not use language. We approach the subjectivity of these people through diagnostic evaluation that investigates their corporeality clinically and experimentally, using pre-established modifications of sensory flows and intersubjective relationships within Snoezelen situations. This is objectified using a structured observation grid. We use a clinical case to emphasize their extreme sensitivity to the sensory and social environment, as well as their vulnerability in terms of bodily and psychic integrity. We present several levels of analysis for their well-being.