Alice: 1 BTC
Bob: 0 BTC
In this state, Alice can send a 0.1 BTC payment to bob, and the channel balances will be: Alice: 0.9 BTC
Bob: 0.1 BTC
Alice and Bob can send each other money, but only up to the amount that they have in the channel. So at this point, Alice can send Bob up to 0.9 BTC, and Bob can send Alice up to 0.1 BTC. Alice: 2 BTC
Bob: -1 BTC
However! When a Lightning Network channel is closed, you divide up the funds from the funding transaction between the parties to the channel. The channel was funded with an on-chain Bitcoin transaction of 1 BTC, so there would be no way to pay out Alice 2 BTC from that initial transaction. Since both parties to a payment channel can close the channel at any time, Alice would be trusting Bob to keep the channel open until he no longer had a negative balance, and avoiding the need for trust is the whole purpose of the Lightning Network in the first place, otherwise we could just trade unenforceable IOUs back and forth.