Final answer:
The most severe negative outcome from an unmatched x-ray beam is patient exposure to radiation without contributing to the diagnostic image, potentially causing cell damage and increasing cancer risk.
Step-by-step explanation:
The most critical negative consequence of an x-ray beam which is not restricted to match the chosen framing method is that an area of the patient is exposed, but an image is not recorded. This unnecessary exposure increases the risk of cell damage and, potentially, cancer because the area that is irradiated does not contribute to the diagnostic information needed. This issue highlights the importance of careful monitoring of radiation dose and proper x-ray technique to minimize the risk to patients.