Why is my multiplayer client teleporting to host location and having host object going missing.

Not sure what kind of netcode stack you are using to build this experience, but this sounds like a common issue devs run into when they don't synchronize their data/input/state correctly from host to client and back.

What is likely happening is when you move/send your input on either client or host, both client and host are receiving the same input and resolving to the same position, thus giving it the illusion as if the client/host "aren't there" once you move around.

You'll need to look into separating the client and host input and movement. Typically this is down through an "isOwner" check in the input update loop, but that can depend on what netcode you're using.

I would recommend looking into the documentation of the netcode you are using and following it carefully to ensure you're not missing a synchronization step - particularly when it comes to input. Look at how to separate input/position with the solution you've chosen.