Yes. If bitcoin drops the channel needs more sats to construct valid payment when user spends.

Until channel closes or user withdraws all funds.

We do this in according to protocol. Host overrides channel state and client accepts it since it increases sats balance on his side. Then the client can send payments up to channel capacity (in asset values). If price increases, then there is enough sats to make payments and there is only asset price in channel states that has to be adjusted.