Based on the scenario you mentioned, it resembles more as Learned Helplessness or Self-Fulfilling prophecy than negative reinforcement.
Learned Helplessness,is a belief that an individual could not make a change to the outcome after being exposed to the aversive stimuli for a number of times (Seligman, 1972).To the point where he/she stop attempting to address the issue as they thought it is inevitable. As an example: a person who failed multiple times for a subject despite constant revision eventually stop trying to take the test because he/she thinks that their effort is "pointless" and do not bother about it anymore since he/she believed their failure is unavoidable.
Self-fulfilling prophecy,is a phenomena when a prediction of an outcome of a situation (directly/indirectly) becomes a reality due to the inclination on false belief of the individual (Madon, Willard,Guyll & Scherr, 2011). Example, if a person thinks he/she is not good in Mathematics and continues to think or feel such way, he/she will likely to fail in an upcoming test. Although the person might not have failed the test, just because of the belief that he/she is terrible at math,which discourage the person to even make an effort to practice and study. Thus, making the individual's statement of "terrible at maths" true.
As for Negative Reinforcement, is when a stimulus that is deemed unpleasant to the individual is removed to increase the possibilities of the behaviour to occur in the future (Skinner, 1953).
In order to better explain negative reinforcement, an example: a teacher decided to cancelled additional classes (removed the unpleasant stimulus) to an individual when he/she did well in exams (increased the likelihood of a behaviour to occur).
Unpleasant stimulus: Additional Class
Behavior to reinforce: Maintains academic grades
Madon, S., Willard, J., Guyll, M., & Scherr, K. C. (2011). Self-fulfilling prophecies: Mechanisms, power, and links to social problems. Social and Personality Psychology Compass, 5(8), 578-590. doi:10.1111/j.1751-9004.2011.00375.x
Seligman, M. E. (1972). Learned helplessness. Annual review of medicine, 23, 407-412. doi:https://doi.org/10.1146/annurev.me.23.020172.002203
Skinner, B. F. (1953). Science and human behaviour. New York: Macmillan.