The content of the session modifies the LLMs "behavior" (token selection) in one way or another during the session, obviously. The effects are localized to the session, they will degrade over time, they will not affect other users, and they are not permanent unless someone decides to finetune the model based on your unproductive interactions.

What actually happens when confronted with harsh negativity depends on the training of the model. Sanitized closed models will shut you down or get you banned. Community finetunes of open models might start begging you for more, daddy.