I'm not aware of truly "forgetting" as in amnesia, but there have been reports that brain damage can disrupt the behavioral pattern of addiction which I think qualifies as what you describe as what "causes the addict to need more and more to be satisfied".
Naqvi et al 2007 reported that:
with brain damage involving the insula, a region implicated in conscious urges, were more likely
than smokers with brain damage not involving the insula to undergo a disruption of smoking
addiction, characterized by the ability to quit smoking easily, immediately, without relapse, and
without persistence of the urge to smoke
Patients in this study had damage from either stroke or from surgical resections for cancer or epilepsy.
Naqvi, N. H., Rudrauf, D., Damasio, H., & Bechara, A. (2007). Damage to the insula disrupts addiction to cigarette smoking. Science, 315(5811), 531-534.
See also this review:
Droutman, V., Read, S. J., & Bechara, A. (2015). Revisiting the role of the insula in addiction. Trends in cognitive sciences, 19(7), 414-420.
However, I'd note that brain damage studies like these are quite complicated because damage to one area is often accompanied by other damage, and few subjects have similar lesions, so I'd be more hesitant than some of these authors are to implicate the insula specifically. Notably, the insula is near subcortical structures and fibers of passage that could also be involved.
Stelten, et al 2008 is a review of neurosurgical attempts to target addiction. These are mostly case studies/series and involved complex cases typically with multiple co-occurring psychiatric conditions. The authors raise ethical concerns with some of the studies, as well, including issues of consent and the permanence of interventions and the lack of control comparisons.
Stelten, B. M., Noblesse, L. H., Ackermans, L., Temel, Y., & Visser-Vandewalle, V. (2008). The neurosurgical treatment of addiction. Neurosurgical focus, 25(1), E5.
You can also find more recent papers and reviews that cite this one on Google Scholar which might be a good place to continue your literature search.