As others have answered, the photo of the Rebbe you are thinking of is all but certainly the Kaliver Rebbe shlita, HaRav Menachem Mendel Traub. As mentioned, the Kaliver Rebbe shlita is a Holocaust survivor, and it is my understanding (as well) that it was during this time he lost his beard. The version of the story I heard is different than Gershon Gold's or Shmuel Brill's versions of the story.
In so far as that makes three slightly, but significantly, different versions of what happened and the details are absent in the Wikipeda page about him, from the general information on the web, and perhaps most significantly from the (now defunct) website apparently established by his Chassidim, it seems to me that the details have been kept quiet out of privacy.
Perhaps until we can find more specific, better sourced, details we should treat it as a private matter as well.