For the following biblatex solution all you need is the name hash of the "special" name (this is a Biber-only feature), you can read more about this in Highlight an author in bibliography using biblatex allowing bibliography style to format it. You will have to use maxbibnames=999 so that all names can be processed.
The solution replaces consecutive less important names by an ellipsis and prints "[et al.]" if we omitted any names.
\newcounter{namesnotimportant}
\newtoggle{ellipsis}
\DeclareNameFormat{first-last-etal}{%
\ifnumcomp{\value{listcount}}{=}{1}
{\setcounter{namesnotimportant}{0}%
\toggletrue{ellipsis}}
{}%
\ifboolexpr{test {\ifnumcomp{\value{listcount}}{=}{1}}
or test {\ifnumcomp{\value{listtotal}}{=}{2}}}
{\iffirstinits
{\usebibmacro{name:first-last}{#1}{#4}{#5}{#7}}
{\usebibmacro{name:first-last}{#1}{#3}{#5}{#7}}}%
{\iffieldequalstr{hash}{e06f6e5a8c1d5204dea326aa5f4f8d17}%% <----- put the correct hash here
{\toggletrue{ellipsis}%
\iffirstinits
{\usebibmacro{name:first-last}{#1}{#4}{#5}{#7}}
{\usebibmacro{name:first-last}{#1}{#3}{#5}{#7}}}
{\stepcounter{namesnotimportant}%
\iftoggle{ellipsis}
{\addcomma\space\textellipsis\togglefalse{ellipsis}\isdot}
{}}}%
\ifnumcomp{\value{namesnotimportant}}{>}{0}
{\toggletrue{abx@bool@more\currentname}}
{}%
\ifboolexpr{
test {\ifnumequal{\value{listcount}}{\value{liststop}}}
and
test \ifmorenames
}
{\andothersdelim\bibstring[\mkbibbrackets]{andothers}}
{}}
\DeclareNameAlias{sortname}{first-last-etal}
\DeclareNameAlias{author}{first-last-etal}
\DeclareNameAlias{editor}{first-last-etal}
\DeclareNameAlias{translator}{first-last-etal}
In the example the special name is "Anne Uthor" and the corresponding hash is e06f6e5a8c1d5204dea326aa5f4f8d17
MWE
\documentclass[british]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{babel}
\usepackage{csquotes}
\usepackage[style=authoryear,backend=biber, maxnames=999]{biblatex}
\usepackage{filecontents}
\begin{filecontents*}{\jobname.bib}
@book{one,
author = {Anne Uthor},
title = {One Author},
year = {2001},
}
@book{twoa,
author = {Anne Uthor and Emma Ditor},
title = {Two Authors -- Important First},
year = {2002},
}
@book{twob,
author = {Emma Ditor and Anne Uthor},
title = {Two Authors -- Important Second},
year = {2002},
}
@book{threea,
author = {Anne Uthor and Emma Writer and William Riter},
title = {Three Authors -- Important First},
year = {2003},
}
@book{threeb,
author = {Emma Writer and Anne Uthor and William Riter},
title = {Three Authors -- Important Second},
year = {2003},
}
@book{threec,
author = {Emma Writer and William Riter and Anne Uthor},
title = {Three Authors -- Important Third},
year = {2003},
}
@book{foura,
author = {Anne Uthor and Emma Writer and William Riter and Catherine T. Ranslator},
title = {Four Authors -- Important First},
year = {2004},
}
@book{fourb,
author = {Emma Writer and Anne Uthor and William Riter and Catherine T. Ranslator},
title = {Four Authors -- Important Second},
year = {2004},
}
@book{fourc,
author = {Emma Writer and William Riter and Anne Uthor and Catherine T. Ranslator},
title = {Four Authors -- Important Third},
year = {2004},
}
@book{fourd,
author = {Emma Writer and William Riter and Catherine T. Ranslator and Anne Uthor},
title = {Four Authors -- Important Fourth},
year = {2004},
}
\end{filecontents*}
\addbibresource{\jobname.bib}
\newcounter{namesnotimportant}
\newtoggle{ellipsis}
\DeclareNameFormat{first-last-etal}{%
\ifnumcomp{\value{listcount}}{=}{1}
{\setcounter{namesnotimportant}{0}%
\toggletrue{ellipsis}}
{}%
\ifboolexpr{test {\ifnumcomp{\value{listcount}}{=}{1}}
or test {\ifnumcomp{\value{listtotal}}{=}{2}}}
{\iffirstinits
{\usebibmacro{name:first-last}{#1}{#4}{#5}{#7}}
{\usebibmacro{name:first-last}{#1}{#3}{#5}{#7}}}%
{\iffieldequalstr{hash}{e06f6e5a8c1d5204dea326aa5f4f8d17}%% <----- put the correct hash here
{\toggletrue{ellipsis}%
\iffirstinits
{\usebibmacro{name:first-last}{#1}{#4}{#5}{#7}}
{\usebibmacro{name:first-last}{#1}{#3}{#5}{#7}}}
{\stepcounter{namesnotimportant}%
\iftoggle{ellipsis}
{\addcomma\space\textellipsis\togglefalse{ellipsis}\isdot}
{}}}%
\ifnumcomp{\value{namesnotimportant}}{>}{0}
{\toggletrue{abx@bool@more\currentname}}
{}%
\ifboolexpr{
test {\ifnumequal{\value{listcount}}{\value{liststop}}}
and
test \ifmorenames
}
{\andothersdelim\bibstring[\mkbibbrackets]{andothers}}
{}}
\DeclareNameAlias{sortname}{first-last-etal}
\DeclareNameAlias{author}{first-last-etal}
\DeclareNameAlias{editor}{first-last-etal}
\DeclareNameAlias{translator}{first-last-etal}
\begin{document}
\nocite{*}
\printbibliography
\end{document}

biblatex-gosta few modifications might be necessary, those are probably along the lines the ones needed in your other question. (If you happen to use a non-standard style it can never hurt to mention that in the question - the most convenient way for helpers is an MWE - so people don't have to go back and rework their answers.) – moewe Mar 07 '16 at 10:42\usepackage[style=gost-numeric,backend=biber, maxnames=999, movenames=false]{biblatex}I got pretty much the output shown above. – moewe Mar 07 '16 at 10:53biblatex-gostformatting: the italic font for author name. Could you help me with it? – KrogZZ Mar 07 '16 at 17:08name:first-lastin the code above byauthorname:last-first.biblatex-gostuses a special format for author names (this is basically the same issue as in your other question). – moewe Mar 07 '16 at 17:12