Can quarks tunnel out of a proton? Can a virtual electron tunnel away from its antiparticle? I know that particles can tunnel through an impassable barrier. But what happens if a quark tunnels out of a proton?
Has that ever been observed?
And what about virtual particles?Can they tunnel away from each other?
 A: As you may know, it is only possible to tunnel if the barrier reaches a maximum and then starts decreasing again, so as to reach an area of potential < than the energy of the particle, where this can exist.
The quarks are bound by the strong force, which is quite weakly binding at very short distances ("asymptotic freedom") but becomes linearly stronger as you get out of the nucleus. The physical reason is that the strong force is mediated by gluons, that, as opposed to photons, can couple and radiate from/to themselves, they do not get sparse but on the contrary keep the 'density' of gluons constant.
So no, free quarks are never observed. This is also called "colour confinement". Strong force interacting particle are assigned a 'colour' charge in the same way as EM interacting particles have an 'electrical' charge - charge is particle physics and similar means something that is conserved. Colour + anti-colour makes colour neutral, same as blue+red+green. In nature you will always find colour neutral particles, never bare coloured particles. Because of the above discussion of the strong force getting stronger as quarks are moved far apart. As you are pulling quarks apart, at some point it would becomes energetically favourable just to convert some energy into the mass of other quark-antiquark pairs and form new bound colour neutral particles.
I should probably add that technically the top quark is found as a bare coloured change. But it's just because its mass is so high that it decays before it has time to form a strong force bound state. 
Virtual particles do not exist, so no they cannot tunnel away from each other. I think you'd be better off asking that as a separate question. 
