In Imagica you cannot safely quit the game, but will then lose your equipment and money. There are however ways to safely leave the game and keep all your characters belongings.

Inns and Cryogenic Centers
Inns are places where the weary traveler may rest while the innkeeper looks after his equipment and treasure.
Specifically, the game will save your equipment while you are logged out. There is a daily cost for renting, based on your equipment. Each item has a per diem charge. The per diem charge is calculated to the nearest second, however -- if you rent at the rate of 24.00 Gd per day, and you come back 39 hours later, you will be charged 39.00 Gd.
A Cryogenic Center will store your items for a one-time charge of four days rent.

Offer and Rent
Offer makes the innkeeper tell you the cost of storing your belongings for one day. Rent stores you belongings and exits you from the game. When you re-enter, you will start where you rented.
Rent files are deleted if you run out of money to pay the per diem charges or after 30 days. Cryogenic-rent files are deleted after 60 days.