As they say, timing is everything. Because a packet can travel around the world in just a few tens of milliseconds, what happens depends on exact timing.
Assuming the new device is on the same network, the last hop router will forward the packet according to its ARP table. If the router has not been able to update its ARP table with the new host MAC address in time, it will forward the packet to a non existent MAC address, and no one will respond. If there is a switch, it will either forward the packet to the old port, or it will flood the packet on all ports. In either case, no one will respond to the packet.
If the router and switch have had enough time to update their tables, the packet will be delivered to the new host.