Perhaps what you are looking for is a combination of \mathrlap
and \smash
which is what is incorporated in the \BraceRight
and \BraceLeft
macros.

However, as HendrikVogt pointed out,
this requires that there be manual spacing added afterwards if there is text that follows it.
To alleviate this issue I have defined two more macros \FracBraceBottomRight
and \FracBraceBottomLeft
which also add the approriate \hptantom
after or before the fraction.

One downside of this this is that you need a different macro in case you desire further options (such as optional braces around either side of the numerator. This can be fixed with a better interface to enable/disable the appropriate brace, but I think that that is more of a question of coming up with the better UI.
References:
Code:
\documentclass{article}
\usepackage{mathtools}
\newcommand*{\BraceRight}[1]{#1\mathrlap{\smash{\left.\vphantom{#1}\right\}}}}%
\newcommand*{\BraceLeft}[1]{\mathllap{\smash{\left\{\vphantom{#1}\right.}}#1}%
% https://tex.stackexchange.com/questions/54023/how-to-compute-exact-width-added-by-left-right
\newcommand{\BracKern}{\kern-\nulldelimiterspace}
\newcommand*{\FracBraceBottomRight}[2]{%
\frac{#1}{#2\mathrlap{\smash{\left.\BracKern\vphantom{#2}\right\}}}}%
\hphantom{\left.\vphantom{#2}\right\}}%
}%
\newcommand*{\FracBraceBottomLeft}[2]{%
\hphantom{\left\{\vphantom{#2}\right.\BracKern}%
\frac{#1}{\mathllap{\smash{\left\{\vphantom{#2}\right.}}#2}%
}%
\begin{document}
Requires manual spacing:
$\frac{a}{\frac{b}{c}}$\quad%
$\frac{a}{\BraceLeft{\frac{b}{c}}}$\quad%
$\frac{a}{\BraceRight{\frac{b}{c}}}$
\bigskip
Auto spacing with \verb|\hphantom|:
$\FracBraceBottomRight{a}{\frac{b}{c}}$%
$\FracBraceBottomRight{a}{\frac{b}{c}}$%
$\FracBraceBottomLeft{a}{\frac{b}{c}}$%
$\FracBraceBottomLeft{a}{\frac{b}{c}}$
\end{document}
\big
,\Big
,... e.g.\frac{a}{\frac{b}{c}\mathrlap{\big\}}}
\documentclass
and the appropriate packages so that those trying to help don't have to recreate it.