<p>No, the minimum rep is and will always be 1 no matter what, that is the minimum necessary to ask a question and will be the minimum for a user after reputation recalculation.</p>

<p>If a user drops bellow 1 the system will compensate for that and after a recalculation it will be back to 1.</p>

<p>There are several reasons for that already discussed in Stack Exchange meta, have a look:</p>

<ul>
<li><a href="http://meta.stackexchange.com/questions/2621/why-does-reputation-have-a-lower-bound-of-1">http://meta.stackexchange.com/questions/2621/why-does-reputation-have-a-lower-bound-of-1</a></li>
</ul>