Beryllium chloride - Highly hydrolysable?
The structures of $\ce{BeX_2}$ where $\ce{X = F}$ or $\ce{Cl}$ can be found in A.F. Wells, Structural Inorganic Chemistry 5th edition, 1984 pages 412 and 1047.  There you will see that while the predicted structures for $\ce{BeX_2}$ are linear (sometimes rationalized with Lewis dot structures displaying double bonds and ignoring formal charge considerations of the halogens).  However, the actual structure of $\ce{BeCl_2}$ in the vapor-phase is a 3-coordinate dimer that converts to the linear structure at higher temperatures.  This behavior supports your 'gut feeling' that the electron deficiency of $\ce{Be}$ should be compensated for by another $\ce{Cl}$ atom.  The dimer network formed in the solid state allows lone pairs from $\ce{Cl}$ to be donated to the $\ce{Be}$ in an attempt to fill the valence shell of beryllium.

The use of a double bond to describe the nature of the $\ce{Be-Cl}$ bond is supported experimental data which shows that the bond length is shorter than expected for a single bond.  

The image below is taken from Inorganic Chemistry by Miessler, Fischer and Tarr, 5th edition.