Auto line break with very long word within table

You could load the xurl package and encase the long number in a \url{...} "wrapper".

(The following code uses a tabularx environment since I'm not familiar with longtabu.)

\documentclass{article}
\usepackage{tabularx,xurl}
\urlstyle{same}
\begin{document} 
\noindent
\begin{tabularx}{\textwidth}{@{} lX @{}}
\hline
\textbf{Head 1} & \textbf{Head 2} \\ 
\hline
12:18:52  & this is a description for the event \\
\hline
12:18:52  &
\url{11111111111111111111111111111111111111222222222222222222222222222222222222222223333333333333333333333333333333333344444444444444444444455555555555555555555555555555555666666666666666666666666666777777777777777777777778888888888888888}\\
\hline
\end{tabularx}
\end{document}

Another solution with seqsplit, xltabular, which combines the functionalities of longtable and tabularx, and makecell to define some vertical padding of cells in the table:

\documentclass{article}
\usepackage{seqsplit, makecell, xltabular}

\begin{document}

{\setcellgapes[b]{3pt}
\setcellgapes[t]{2pt}\makegapedcells
\noindent\begin{xltabular}{\textwidth}{|c|X|}%|
    \hline
    \textbf{Head 1} &
    \textbf{Head 2}
    \\ \hline
    12:18:52 & this is a description for the event \\\hline
    12:18:52 & this is a description for the event \\\hline
    12:18:52 & this is a description for the event this is a description for the event this is a description for the event this is a description for the event this is a description for the event this is a description for the event this is a description for the event this is a description for the event this is a description for the event this is a description for the event this is a description for the event this is a description for the event this is a description for the event this is a description for the event this is a description for the event this is a description for the event this is a description for the event this is a description for the event \\\hline
    12:18:52 & \seqsplit{ 111111111111111111111111111111111111112222222222222222222222222222222222222222233333333333333333333333333333333333444444444444444444444%
    55555555555555555555555555555555666666666666666666666666666777777777777777777777778888888888888888} \\\hline
\end{xltabular}}

\end{document} 

The problem is that the number is not in the list of words that tex uses to determine possible break points of words, but one can manually add them by placing \- at each point where the number can be broken across lines:

\documentclass{article}

\usepackage[english]{babel}

\begin{document}

\begin{tabular}{|p{1cm}|p{5cm}|}
  This text will be wrapped & Some more text \\\hline
  this & 1\-111\-111\-1111\-111\-111\-11\-111\-111\-111\-111\-111\-111\-122\-22\-222\-22\-222\-22\-22\-222\-22\-22\\\hline
\end{tabular}

\end{document}