The short answer is no. Have a look at the wikipedia article on dissipation of black holes.
quote: Unlike most objects, a black hole's temperature increases as it radiates away mass. The rate of temperature increase is exponential, with the most likely endpoint being the dissolution of the black hole in a violent burst of gamma rays.
The possibility of micro black holes from extra dimensions in some string models still has them dissolving thermodynamically into elementary particles as soon as they are formed.
Edit: Herein I have been replying to the question stated clearly in the last sentence: Is it possible that elementary particles are ultimate nuggets of the final stages of black holes after emitting all the Hawking radiation it could? Not to the different question that people seem to be replying to: "are black holes like elementary particles."
A yes answer to the latter, does not reply to the former, i.e. whether quarks and leptons are the nugget, what is left over, from a black hole. A yes answer to this last would offer the intriguing model of the snake eating its tail, maybe quite probable in some new more encompassing theory, but not foreseen now, at least from the answers given. If after shedding innumerable quarks leptons and photons and entropy on the way, a black hole ends up as an electron (for example) in an identifiable quantum mechanical history.By this last I mean something similar to a decay chain in nuclear cascades.