she sent to G if she never closes
her channel with B?
Example of Initial state of your piece of LN, channels are enclosed in parentheses:
A(1:0)B(3:2)C(4:1)D(1:2)E(5:6)F(2:0)G
After A pays 1 BTC to F (intermediaries don't charge fees):
A(0:1)B(2:3)C(3:2)D(0:3)E(4:7)F(1:1)G
Each channel contains the same amount of BTC as before. Note, that A can't pay F again through this route, because A's balance is 0, and D's balance (in A->G direction) is also 0.
If G closes his channel with F, they will receive onchain their shares of their channel and that's it.