As of writing this, the literature on hypnosis and cognitive aspects of brain injury is easily summarized. I'll write this up in greater detail in a paper, but I thought that it would be useful to make a few pointers to the relevant literature here so that it is accessible to everyone. There are also a number of case-studies, but I will not include these here since most of them target motor-rehabilitation.
Hypnosis as rehabilitation
Take-home: There are (large) positive effects of hypnosis on cognition following acquired brain injury.
Lindeløv, J. K., Overgaard, R., & Overgaard, M. (2017). Improving working memory performance in brain-injured patients using hypnotic suggestion. Brain, 140(4), 1100–1106. https://doi.org/10.1093/brain/awx001.
Our study, showing a large specific effect on working memory performance of hypnotic suggestions involving the return to pre-injury (or normal) functioning. It's an RCT with a total of 68 patients stratified to targeted hypnosis, an active control, and a passive control. The effect of four and eight treatment sessions is assessed with long-term follow-up.
Sullivan, D. S., Johnson, A., & Bratkovitch, J. (1974). Reduction of behavioral deficit in organic brain damage by use of hypnosis. Journal of Clinical Psychology, 30(1), 96–98. https://doi.org/10.1002/1097-4679(197401)30:1<96::AID-JCLP2270300133>3.0.CO;2-A.
Later we discovered this similar study had been carried out by Sullivan et al. (1974). The Sullivan study, however, had an intervention consisting of just seven sentences repeated twice - probably less than two minutes! They obtained a small positive effect on the Picture Completion task from the WAIS battery but not on the Binder-Gestalt test. They had a quite small sample, and the two-page article leaves many details unreported.
Cui-ping, L. I. (2011). Influence of hypnosis therapy on recovery of hemorrhagic stroke. Journal of Taishan Medical College, 1, 025. http://en.cnki.com.cn/Article_en/CJFDTOTAL-TSYX201101025.htm (see my English translation and comments)
An RCT showing large effects (SMD = 1.0 to 1.7) on Barthel, anxiety, and depression in stroke patients given ten sessions of hypnosis between one and twelve weeks after the injury onset. The study is relatively large with 120 treatment-as-usual patients of which 49 had additional adjunctive hypnosis. It was published in Chinese in a Chinese journal with impact factor 0.1, and it is unclear whether it was peer-reviewed. In general, there are many reasons to be skeptical of the quality of this paper. Nonetheless, everything else being equal, it does increase the probability that hypnosis can improve cognition following acquired brain injury. With the help of Chinese friends, I got hold of the paper and helped reading it. I've added a link to my translation in the reference above, containing comments to clarify particular unclear sections and dubious statistics.
Suggestibility following acquired brain injury
Take-home: Brain injured patients are as suggestible/hypnotizable as the general population
Laidlaw, T. M. (1993). Hypnosis and Attention Deficits After Closed Head Injury. International Journal of Clinical and Experimental Hypnosis, 41(2), 97–111. https://doi.org/10.1080/00207149308414541
No difference in suggestibility on the HGSHS:A for young concussion patients relative to healthy controls.
Kihlstrom, J. F., Glisky, M. L., McGovern, S., Rapcsak, S. Z., & Mennemeier, M. S. (2013). Hypnosis in the right hemisphere. Cortex, 49(2), 393–399. https://doi.org/10.1016/j.cortex.2012.04.018
No difference in suggestibility between middle-aged stroke patients relative to young controls on AMSH.
Lindeløv, J. K., Overgaard, R., & Overgaard, M. (2017). Improving working memory performance in brain-injured patients using hypnotic suggestion. Brain, 140(4), 1100–1106. https://doi.org/10.1093/brain/awx001
Our study tested 49 brain injured patients on SHSS:C but did not compare them directly to healthy controls. However, looking at SHSS:C norms from other countries, the suggestibility of the patients seemed normal.
Hypnosis to induce "brain injury"
Take-home: healthy subjects can be hypnotized to play the role of brain injured patients, but they are probably not realistic brain-injury models.
Fromm, E., Sawyer, J., & Rosenthal, V. (1964). Hypnotic simulation of organic brain damage. The Journal of Abnormal and Social Psychology, 69(5), 482. http://psycnet.apa.org/index.cfm?fa=buy.optionToBuy&id=1965-08145-001
Hypnotized subjects to believed that they had sustained an organic brain injury. After "hypnotic brain injury," these subject were judged to be more "organic" by blinded neuropsychologists than under "hysterical" and no-hypnosis conditions, in which they were judged to be non-injured.
Wagstaff, M., Parkes, M., & Hanley, J. R. (2001). A comparison of posthypnotic amnesia and the simulation of amnesia through brain injury. International Journal of Psychology and Psychological Therapy, 1(1), 67–78. http://www.ijpsy.com/volumen1/num1/5.html
Like Fromm (1964), but adds malingering-detection tests to the test battery, showing that "hypnotically brain injured" healthy subjects indeed do act as malingerers, not as real brain injured patients.