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.

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

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

 * http://meta.stackoverflow.com/questions/2621/why-does-reputation-have-a-lower-bound-of-1