I'd like to know if there is some font to produce the cursive Cyrillic characters as in the image
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This may partially explain the lack of easy to find fonts supporting cursive Cyrillic characters:
The early Cyrillic alphabet is difficult to represent on computers. Many of the letterforms differed from modern Cyrillic, varied a great deal in manuscripts, and changed over time. Few fonts include adequate glyphs to reproduce the alphabet. In accordance with Unicode policy, the standard does not include letterform variations or ligatures found in manuscript sources unless they can be shown to conform to the Unicode definition of a character.
The Unicode 5.1 standard, released on 4 April 2008, greatly improves computer support for the early Cyrillic and the modern Church Slavonic language. In Microsoft Windows, Segoe UI is notable for having complete support for the archaic Cyrillic letters since Windows 8.