The tachyonic string mode in perturbative bosonic string theory indicates that the "vacuum", flat Minkowski $\mathbb{R}^{25,1}$, is not really a vacuum. What is conjectured about tachyon condensation in this theory? Do we expect the theory to have a vacuum? Is there any way the condensate might generate fermions dynamically?
[Edit] Since Chris Gerig asked for more background: Tachyons, sadly for Star Trek writers, are typically an indication that the state you think is the vacuum of your system is, in fact, not the vacuum. This is because you can act on the ground state with a tachyon creation operator and get a new state with lower energy. For example, the Higgs potential is $$V(\phi) = \frac{1}{2}\lambda (|\phi|^2 - c^2)^2 = -\lambda c^2 \phi^2 + \frac{\lambda}{2} \phi^4 + const$$ If you do perturbation theory around $\phi_0 = 0$ instead of around one of the true minimum $\phi_0 = C$, with $|C| = \mu^2$ , you'll find the creation operators in $\phi_{pert} = \phi - \phi_0$ create tachyons, with negative mass-squared $m^2 = -\lambda c^2$. Create enough of these tachyons, and you'll turn the state $|\phi_0 = 0\rangle$ which you thought was the vacuum into one of the true vacua $|\phi= C\rangle$.
Bosonic string theory in 26d has tachons: the most basic closed and open string excitations, created by vertex operators with no derivatives. So it's a natural question to wonder about: what state do we get if we add tachyons to the false perturbative vacuum? Does this process converge? This is a pretty hard question to answer, since in bosonic string theory we don't have SUSY-protected quantities that we can compute to check our predictions. Which is why I asked what had been conjectured.
