Okay, I anybody tries something, here what i found out so far... When I changed PlType for all players I added from 4 to 5 things have changed. After World Series had finished I was able to press enter and Adwance to Season Awards, then to Players Awards, but it crashed when I wanted to advance to Teams Awards screen. So I started the game again, loaded crashed Franchise and it took me to Offseason Tasks Screen, I advanced through all of them, then simulated new season (2013) and postseason as well, and then there was no crash at all and I could advace to next season (2014) and so on...
So if you have ideas what is that about... help
EDIT:
Okay so I've tried this with various teams and numerous times and not always it worked like i wrote above... Sometimes it crashed right after WS, sometimes it went few screens and crashed, then I could continue after restarting game, but sometimes it didn't start the new season, sometimes it started and simulated new season but the next one was problem... So generaly we could say that end of Franchise season and/or begining of new one is somehow a problem...