This is all IMO, ok? I have switched one time. Positions that were eligible were transferred from one broker to another. All of my positions were eligible.
Those that were not clearninghouse elegible (DTC? eligible? there is a specific term this use for this I forget what it is)-- well, the different brokers handle different positions in their own way. I have seen forced sell outs at market, no tranfer at all, printed certificates mailed to shareholder, screw ups, all kinds of crap when their electronic tranfer process does not work for non-eligible securities. Mostly this is from reading about other peoples' misfortunes.
Sounds scary. But the bottom line is that brokers don't like written complaints. It makes them look bad. They want to hit back when customers hit them.