What is the ruling on the a woman living alone in a Western country marrying without a guardian, and who would be her guardian in this situation?

For a girl living alone, it does not mean she has no guardian (wali). If she has a guardian in another country and he cannot attend the marriage contract, he may appoint someone to conduct the contract. If she has no guardian and is a Muslim, then her marriage method is explained in Fatwa (definition) no. 73641. If she is a chaste woman of the People of the Book, then their bishops are the ones who handle her marriage. We emphasize the importance for a Muslim to choose a righteous Muslim woman who will assist him in matters of his religion and worldly life, and that he should seek guidance from Allah (istikharah). Although marriage to a woman of the People of the Book is permissible in principle, it is disliked for reasons mentioned in Fatwas no. 32475 and 100335.