Panhandle is a narrow strip of territory projecting from the main territory of one state into another state. Google translates panhandle as попрошайка, попрошайничать (beggar, beg). Is there a one Russian word for panhandle in a geographical context, as in "Florida panhandle" for example.
Actually, the direct translation for "panhandle" would be "ручка скоровородки" - this is the reason why it is called that way in English in first place. However we don't have a 100% matching term in Russian.
If one want to talk of specifically of Florida panhandle, one would just say something like "неполуостровная часть Флориды", or "материковая часть Флориды". Technically, panhandles are salients, that is "elongated protrusions of a geopolitical entities, such as a subnational entity or a sovereign state". This term is translated to Russian as "выступ" but de-facto it's usage (in this context) is not that wide-spread as usage of panhandle in English.
For instance, "Aляскинский выступ" is nowhere close in usage to Alaska panhandle, "Юго-Восточная Аляска" is way more popular. "Северный выступ Западной Виргинии" (another example mentioned in Wikipedia) sounds very artificial - actually in each individual case the actual Russian term varies. Though I have to admit that I miss a Russian counterpart.