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The 09-localhost ClientState maintains a single field used to track the latest sequence of the state machine i.e. the height of the blockchain.
The 09-localhost ClientState is instantiated in the InitGenesis handler of the 02-client submodule in core IBC. It calls CreateLocalhostClient, declaring a new ClientState and initializing it with its own client prefixed store.
It is possible to disable the localhost client by removing the 09-localhost entry from the allowed_clients list through governance.

Client updates

The latest height is updated periodically through the ABCI BeginBlock interface of the 02-client submodule in core IBC. See BeginBlocker in abci.go.
The above calls into the 09-localhost UpdateState method of the ClientState . It retrieves the current block height from the application context and sets the LatestHeight of the 09-localhost client.
Note that the 09-localhost ClientState is not updated through the 02-client interface leveraged by conventional IBC light clients.