Generative AI (genAI) is increasingly being integrated into children's everyday lives, not only through screens but also through so-called "screen-free" AI toys. These toys can simulate emotions, personalize responses, and recall prior interactions, creating the illusion of an ongoing social connection. Such capabilities raise important questions about how children understand boundaries, agency, and relationships when interacting with AI toys. To investigate this, we conducted two participatory design sessions with eight children ages 6-11 where they engaged with three different AI toys, shifting between play, experimentation, and reflection. Our findings reveal that children approached AI toys with genuine curiosity, profiling them as social beings. However, frequent interaction breakdowns and mismatches between apparent intelligence and toy-like form disrupted expectations around play and led to adversarial play. We conclude with implications and design provocations to navigate children's encounters with AI toys in more transparent, developmentally appropriate, and responsible ways.