What am I overlooking on this switch?

I'm looking to understand how a certain switch is reaching outside its network.

I've got a switch (2960) in my room office, no ip routing enables, no default-gateway set, no management port. It's assigned let's say 10.0.0.2 /25 on a vlan. That's hooked up to a multiplayer switch to get it out. Now my PC is 10.0.0.200/25. My PC is able to reach it and management, and how is what i'm trying to figure out.

I thought it might be proxy arp, but testing disabling that didn't stop things. It's disabled at the gateway router as well.

One person I talked to said that if it's sitting in the same segment, it would be able to still route out with that multilayer switch. I don't quite understand this though.

Is there something I'm missing? My understanding is that it should just drop that packet when it sees it has no path back, simple as that. Am i be stupid?

Edit: Changed /23 to /25