Suppose that I have a lump of a radioactive material, like Uranium-235. I put it in an ideal box, which perfectly isolates the inside from the outside - no radiation escapes the box and the outer surface of the box does not change in any way. The box is thrown by an astronaut with velocity $v_0$. The mass of the box and the lump is $m_0$.
As time goes by, the radioactive material decays. After time $t$ has passed, the total mass of the box and the partially decayed lump has fallen to $m_1$. Some mass has "evaporated" and turned into other forms of energy, for example by alpha decay of Uranium-235.
Given that the conservation of momentum mandates that $m_0v_0=m_1v_1$ and that the mass has decreased, it seems like the velocity of the box had to have increased.
This seems strange because for an outside observer it looks like the black box has spontaneously accelerated without any external force acting on it. This would even allow for creating a simple, yet effective, rocket engine - just take some uranium onboard and see the rocket start to fly faster all by itself.