The purpose of any multi-asset can be arbitrary, however it's important to remember that like ada a multi-asset is part of the transaction and needs to be handled and balanced in the same way.
Multi-assets will cause no issue whether located in the issuers wallet or the Exchanges wallet it will exist until otherwise redeemed, used or eventually burnt.
The decision of what to do with a multi-asset lyes with the exchange or 3rd party wallet and even more specifically with an exchange that manages their own UTXO’s.
cardano-wallet uses a UTXO algorithm to handle and manage UTXO’s therefore a multi-asset living on the blockchain and being handled by cardano-wallet can easily go unnoticed.
Choosing a UTXO means having to account for the asset attached to that UTXO. If this extra input is not handled correctly an out of balance error will occur.
What you do with the Native asset is up to you, you can either return the native asset back to the sender only if you know the address of course or alternatively you can move the native asset in and address in your wallet adhering to the network guidelines and min UTXO value.
For more information on creating and balancing a transaction with a native asset attached please see the following documentation here