I don't know the type of game, but I have a suggestion.
If the player plays some levels or a story mode offline, he can find items and so on.
He can use them in the online mode. The ingame money is saved on a server. The items he can find in the offline mode aren't good and he have to upgrade them in the online mode to make them better.
The player only can get ingame money in the online mode.
This would be my suggestion.
It isn't a really good idea, but I hope I could help you.