\documentclass{article}
%\usepackage[designv,forcolorpaper,tight*]{web}
\usepackage{hyperref}
\usepackage{forms16be}

\defUniStr{VDV}{\u03B1 cos(\u03B8)}
\defUniStr{TU}{Don \u\EURO Story "\u03B1 cos(\u03B8)"}

\makeatletter
% Define two new keys udefault and uvalue to take big-endian values
\define@key{Field}{udefault}{%
  \def\Fld@udefault{#1}%
}
\define@key{Field}{uvalue}{%
  \Hy@pdfstringdef\Fld@uvalue{#1}%
}
\let\Fld@udefault\ltx@empty
\let\Fld@uvalue\@empty
\def\PDFForm@Text{%
  /Subtype/Widget%
  \Fld@annotflags
  \Fld@pageobjref
  \Fld@annotnames
  /FT/Tx%
  \Fld@flags
  /Q \Fld@align
  /BS<</W \Fld@borderwidth\space /S /\Fld@borderstyle>>%
  \ifcase0\ifnum\Fld@rotation=\z@   \else 1\fi
          \ifx\Fld@bordercolor\relax\else 1\fi
          \ifx\Fld@bcolor\relax     \else 1\fi
          \space
  \else
    /MK<<%
      \ifnum\Fld@rotation=\z@
      \else
        /R \Fld@rotation
      \fi
      \ifx\Fld@bordercolor\relax
      \else
        /BC[\Fld@bordercolor]%
      \fi
      \ifx\Fld@bcolor\relax
      \else
        /BG[\Fld@bcolor]%
      \fi
    >>%
  \fi
  /DA(/Helv \strip@pt\Fld@charsize\space Tf%
      \ifx\Fld@color\@empty\else\space\Fld@color\fi)%
% Determine which key to used based on uvalue and udefault
\ifx\Fld@udefault\ltx@empty
  /DV(\Hy@escapestring{\Fld@default})\else
  /DV<\Hy@escapestring{\Fld@udefault}>\fi
\ifx\Fld@uvalue\@empty
  /V(\Hy@escapestring{\Fld@value})\else
  /V<\Hy@escapestring{\Fld@uvalue}>\fi
  \Fld@additionalactions
  \ifnum\Fld@maxlen>\z@/MaxLen \Fld@maxlen \fi
}
\makeatother

\def\cs#1{\texttt{\char`\\#1}}
\let\pkg\textsf

\parindent0pt \parskip6pt

\begin{document}
\begin{Form}

The \pkg{hyperref} package does not support initializing form fields with big-endian, but it is possible
to modify some \pkg{hyperref} core code to get the desired result. The maintainer can take this example
and generalize it to all appropriate form fields and properties, it there is a demand.

\def\LayoutTextField#1#2{#2}
\TextField[uvalue={\unicodeStr(VDV)},udefault={\unicodeStr(VDV)}]{textfield}

\end{Form}
\end{document}