Constraints on new unknown stable fermions? This question is rather speculative, but I would like to ask it anyway. What are the constraints on possibility of discovering new unknown stable fermions of some sort in the future? 
If I am not wrong, we can exclude particles lighter than ~400 GeV, otherwise they would already show  in some way in experiments performed so far. Or they would have to interact very little with both our matter and electromagnetic radiation, like axions do. Are there any other strong limits? (on mass, charge, spin, coupling to strong/electroweak sector, etc.)
I am particularly interested in solid constraints, I am aware that according to most standard theories, no new stable fermions are probably expected, but I am interested what can we really rule out.
 A: As CuriousOne mentions in the comment, if the new fermion has no charge under any of the gauge symmetries then it will not interact with anything (except gravitationally) so we barely have any constrains on such particles.
On the other hand, if you are thinking more about the lines of a fermion that is "similar" to $e, \mu$ or $\tau$, but just heavier, then in reality your are asking for the constraints on a fourth generation. It is reasonable to expect that such a fermion would be accompanied by a light neutrino, in the same way that the others do. However, the number of light neutrino families has been measured experimentally to high precision, see for example:
http://pdg.lbl.gov/2014/reviews/rpp2014-rev-light-neutrino-types.pdf .
So this proposition is ruled out.
Therefore, the new fermion will be accompanied by a heavy neutrino (or no neutrino at all). Then you have to explain why this would be the case and the constraints on the new particle will be dependent on the model you propose. 
A: In supersymetry every particle from the standard model has a superpartner. But photons, gluons and W-and Z-bosons don't have photinos, gluinos, winos ,and zinos as superpartners but neutralinos which are a bit of  photinos,gluinos winos ,and zinos. The lightest neutralino which is a fermion is probably stable. They probably are neutral, have no color charge and interact by the weak interaction.
They also interact through gravity. They could be a component of dark matter. There are 3 other neutralinos but they are unstable. Their mass is unknown. 
