It doesn't affect Jamie's employment; just her weight. If you switch the statue and Jamie doesn't get fired, she'll get somewhat chubby. If you switch the statue and she gets fired, she'll get extremely fat. (If you don't switch the statue and she gets fired she'll get very fat, but not as fat as if you did switch the statue.)
If you've moved in with Jamie at some point you'll get an option to snoop around her home, and you'll see the statue. Go to Shadowed Curios to ask about it, and when you get back home you can log into the computer to order a duplicate statue; it will arrive the next day. Eventually in a few days you'll get an option to snoop around again and switch the statue. She'll noticeably gain weight in a few days; this will be apparent in any scenes with her. If you also get her fired when the statue has been switched, she'll gain a LOT of weight over time.