Hi,
We have circulated board games for almost a year. In general, they come back intact, with all pieces.
We do a few things to help with that. Our board games go out for 2 weeks. We tape the box edges but also put them in plastic storage cases (mostly because ours go in our delivery trucks between branches). All games have a label that gives a list of all the game's contents. It helps patrons make sure they have everything. We also laminate the rule books for each game. Any cards that can be sleeved are, we purchase MayDay Games card sleeves. All of these things cost quite little compared to some of the games we circulate.
As for replacement pieces, it really depends on the game. We try hard to make it as convenient and cost-efficient for patrons as possible. For instance, when a card for Ticket to Ride was chewed on by a patron's dog, they were willing to pay for the whole game, however we contacted Days of Wonder (the manufacturer), and they actually sent an entire deck of replacement cards free. For other games, I always look online for replacement parts first. There are a lot of sites that you can purchase pieces from.
Feel free to contact if you have any other questions.
Good luck with your games!