Here's an idea how about you have to feed your bomy pet and the food costs money. So you must work at something for a few minutes/hours to get enough money to feed your bomy pet then he stays with you. But if you fail to feed it he runs away and becomes wild again waiting for a new owner.
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Y'know sometimes even my lucky rocketship underpants don't even help.
Although in that case there should for example be a place where you can leave your bomy for some Gralats and that it won't get hungry while it is in that place, otherwise people would have to stay online for 24 hours a day.