It's hard to be in a compartment for a couple of days without some type of communication taking place. Security Common sense is your best protection. Keep anything you don't want to loose on your person at all times. There are lockers under the seats and you can have the attendent lock your compartment when it is unoccupied. You can also lock the door at two points from the inside.
Some people even add a belt for extra protection.
There are theives on the train just like anywhere else. Don't look like a target and you are less likely to be one. More than anything the atmosphere is family-like. The trains are a primary means of transportation for common Russian people. There will be all types of people aboard from whole families to scientists to older children going to visit relatives.