Does radioactivity affect chemical reactions?

Do compounds of radioactive elements show a different behaviour? What happens when the radioactive part of the given compound decays? e.g. Radium chloride; what happens to it when radium decays?

Answer

During the nuclear reaction, the atomic number Z (and therefore chemical identity) changes (transmutation). In your example, $\ce{RaCl_2 -> \alpha^{2+} + RnCl_2^{2-} -> He + RnCl_2}$.

Radon being noble gas would react further, e.g. $\ce{RnCl_2 -> Rn + Cl_2}$

If the decaying atom would be a transition metal with ligands, it's properties should not change so drastically so that the ligands will stay attached.