Are you perhaps interested in something like:

Similar results could be achieved by means of the hobby
package. Here is the code:
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\begin{document}
\begin{figure}[H]
\centering
\begin{tikzpicture}[use Hobby shortcut]
\draw[orange, very thick] (0,4) .. (-0.1,3.5) .. (-0.3,3) .. (-0.65,2.7) .. (-0.55,2) .. (-0.2,1.2) .. (0,0) .. (0.2,0.4) .. (1,1) .. (0.8,2.3) .. (0.5,2.8) .. (0.25,3.5) .. cycle;
\foreach \place/\el in {{(0,1.2)/+},{(0,3)/-},{(0.5,2.5)/+},{(0.7,1)/-},{(-0.2,2.5)/-},{(0.1,2)/+},{(0.6,1.5)/+}}
\node at \place {\ensuremath{\el}};
\end{tikzpicture}
\caption{Avalanche Multiplication}%
\label{fig:avalanche}%
\end{figure}
\end{document}
From the comments seems clear I misunderstood the question; a belated attempt to remedy (of course with hobby) :):
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\begin{document}
Completely closed:
\begin{center}
\begin{tikzpicture}
\draw[orange, very thick] (0,4) to[curve through={(-0.45,2)..(-0.9,0) .. (0.9,0) .. (0.45,2)}] (0,4);
\foreach \place/\el in {{(0,1.2)/-},{(0,2.8)/-},{(-0.5,0.8)/+},{(0.55,1)/-},{(-0.2,1.7)/-},{(0.1,2)/+},{(0.55,1.5)/+},{(0.2,0.5)/+},{(-0.2,0.2)/-}}
\node at \place {\ensuremath{\el}};
\end{tikzpicture}
\end{center}
Not closed:
\begin{center}
\begin{tikzpicture}
\draw[orange, very thick] (-0.035,4) to[curve through={(-0.45,2)..(-0.9,0) .. (0.9,0) .. (0.45,2)}] (0.035,4);
\foreach \place/\el in {{(0,1.2)/-},{(0,2.8)/-},{(-0.5,0.8)/+},{(0.55,1)/-},{(-0.2,1.7)/-},{(0.1,2)/+},{(0.55,1.5)/+},{(0.2,0.5)/+},{(-0.2,0.2)/-}}
\node at \place {\ensuremath{\el}};
\end{tikzpicture}
\end{center}
\end{document}
Result:

Since Garbage Collector posted a very nice PSTricks gif animation, it sounds to me that we should have also a TikZ-based version. Basically, the standalone
class with the tikz
option allows to create several pdf pages, the base of the animation. The +
and -
signs change position in each page because their coordinates are generated by random numbers, the function rnd
which generates number from 0 to 1. That's why each time a random number is created, it is multiplied by a constant factor that amplifies and bounds the positions in which each sign will be placed.
\documentclass[tikz]{standalone}
\usepackage{tikz}
\usetikzlibrary{hobby}
\begin{document}
\foreach \number in {1,...,20}{
\begin{tikzpicture}[scale=2]
\draw[orange, very thick] (0,4) to[curve through={(-0.45,2)..(-0.9,0) .. (0.9,0) .. (0.45,2)}] (0,4);
\foreach \place/\el in {{(rnd*0.8,rnd*1.05)/-},{(rnd*0.05,rnd*2.8)/-},{(-rnd*0.5,0.8)/+},{(rnd*0.55,rnd*1.1)/-},{(-rnd*0.2,rnd*1.7)/-},{(rnd*0.4,1.8)/+},{(rnd*0.55,1.5)/+},{(rnd*0.9,rnd*0.9)/+},{(-rnd*0.9,rnd*0.4)/-}}
\node at \place {\ensuremath{\el}};
\end{tikzpicture}
}
\end{document}
Result:
