Broadcast question

Hey folks,

For some reason, I'm struggling to recall how this plays out.

Say we have an access switch with VLAN16 on it. A host wants to talk to the network for the first time and does an ARP to get the MAC of the DGW. Access switch floods this out all ports including the trunk to the core, which serves as the DGW through an SVI. However, the core has trunks with VLAN16 allowed on it as well.

Does the core forward that broadcast out still to the other trunks, or does it simply respond to the broadcast?

This is relevant to me because our network has VLANs allowed on trunks that connect to switches that do not have the VLAN on them. I'd like to fix that regardless, but it got me thinking about this question!