Can't say I've had any problem with any of my games in offline mode. As long as a game doesn't have additional 3rd party DRM that needs online authentication, it shouldn't be a problem.

If a game is running say, Ubisoft's DRM that requires internet connection all the time, then the problem is with that game itself. Steam or not you can't run such game if your internet service is down.

try deleting everything in the steam folder except for the steam application icon and steamapps folder

let it redownload the client itself