Dysprosody

Dysprosody is an extremely rare and little understood neurological speech disorder. Also known as pseudo-foreign accent disorder, it is caused by damage or injury to the brain that causes the patient to be unable to control the way in which they speak, but does not effect the use or comprehension of language. It causes changes in speech volume and rhythm that often creates the sensation that a person is speaking with a foreign accent.

Dysprosody is the rarest neurological speech disorder but can also be caused by brain damage (from trauma, lesions, or stroke) and can be associated with Parkinson's disease.

An example would be a native English speaker who acquires this disorder and their speech changes and sounds as if they have an English or Chinese accent.