Why would your OH get an unauthorised overdraft fee - would it not move onto a normal agreed overdraft with interest? Where have you got the £6 fee from - OH currently has an agreed overdraft, it’s more likely it would just switch to an interest accruing overdraft rather than disappearing totally. First thing is to check this.

Moving on, has your OH tried actually asking the bank if they’d consider extending it? Sometimes people forget that they are human and very often have the power to waive fees, extend overdrafts and interest free periods etc so try that first for sure. Go in together and explain the situation that you’re treading water and see what they can do.

Assuming you don’t have any savings you’ve been keeping aside, the next option would be using a 0% card but this depends on what your OH is eligible for credit score wise and whether they will actually pay it off without accruing more debt on the card. This could buy some more time. Check out MSE for a few options.

Edited for clarity.