What are the most common failure modes of Solid State Relays?
It is like what is first failure mode on all cars. 

The Modes depend on Root Causes; Bad design margin for application, bad solder process with environmental stress, poor OEM quality controls (Qualification Test verification)  

Use historical data only for each source and P/N then verify Design and Process with  a good DVT &amp; PVT test plan.  Otherwise low confidence in your results in poor estimates.

If you need to design a circuit with likely potential for stuck ON switch then you need to do by a redundant safety switch means.