In your code snippet, the following works, although it may require some tweaking for more complicated examples:

\documentclass{article}
\begin{document}
\begin{tabbing}
Person1: \underline{Long info about Person1} \= \\
Person2: \underline{Shorter info} \> \\
Person2: rlap{\underline{\hphantom{Long info about Person1}}}Shorter info
\end{tabbing}
\end{document}
The reason why this works is because Person1 is similar in width to Person2. If this is not the case, you can always use an extra tab marker \= to identify this location.
\rlap allows for a right overlap (of width 0pt), while \hphantom only takes the horizontal width into consideration (without typesetting anything). That is, no height, and therefore also no descenders. If you have descenders within Shorter info, a regular \phantom should suffice.
Here's an alternative view on something similar, this time using tabular:

\documentclass{article}
\begin{document}
\begin{tabbing}
First person: \hspace*{2em} \= \underline{Long info about Person1} \= \\
Second person: \> \underline{Shorter info} \> \\
Second person: \>\rlap{\underline{\hphantom{Long info about Person1}}}Shorter info
\end{tabbing}
\noindent\begin{tabular}{@{}l@{\hspace*{2em}}l@{}}
First person: & Long info about Person1 \\ \cline{2-2}
Second person: & Shorter info \\ \cline{2-2}
\end{tabular}
\end{document}
Person2: \underline{Shorter info }\>yet? – q9f Jun 08 '12 at 15:57\underline{Shorter info}without showing a break? Note that\underlineis put below the depth of its contents. SinceShorter infocontains no descenders, it will be placed higher than that ofLonger info. – Werner Jun 08 '12 at 16:02underline{Shorter info}is not desirable. – Victor Proon Jun 08 '12 at 17:04