If she does not work in the US, Does not have a US bank account, does not get paid in the US, is not a US citizen and holds no US property she cannot be taxed in the US.
She can get a SSN but on your tax return you list her as a NON-RESIDENT ALIEN. This is how my husband and I did my taxes for years and he never paid US taxes because he was not required to. I was listed married and took him as a dependent…this was all legal and how I was required to do it.
We got the SSN number for him in the UK and that is also hoe he was listed as a non-resident alien and I was listed married but filed separately.
