Security of secure two-party computation with a trusted dealer during offline phase?
This is the so-called Common Reference String (CRS) model, or Correlated Randomness model. A good reference to it is the paper On the Power of Correlated Randomness in Secure Computation.  

Secure multiparty computation (MPC) can be expensive (in terms of computational or communication complexity) when a trusted party (the one doing all the computation in secrecy) doesn't exist. Secure MPC is easy when a central trusted party can execute all in secrecy, but this is what everybody doesn't want. 

With the CRS we have an interesting model: the creator of the randomness is usually a trusted party. But, this trusted party can be unaware of the computation the parties intend to execute. So the model separate who knows the joint randomness, and who execute the computation. And by supposing a CRS, we can reach secure MPC at a low price. Therefore, the belief that the CRS can't be compromised is a cornerstone of the model: it doesn't compute, but if it leaks the randomness, everything falls flat.