You can define arbitrary preference rules. For example, the conversion doesn't have to be 1-to-1.
In the case of Square's IPO, Series E preferred had a provision giving them extra free common stock to make up the gap if it IPO'd below $18.55 (which it did).
You can, and I may be wrong here, but I seem to recall that one has to call out these sorts of options in the S-1. It is material to people investing in the IPO.
In the case of Square's IPO, Series E preferred had a provision giving them extra free common stock to make up the gap if it IPO'd below $18.55 (which it did).