Particularly where (as in the United States) foreign branches are forbidden by local law from accepting retail deposits, it might seem that there are minimal risks to the host country if the parent bank (and thus the local branch) fails.
However, U.S. experience with foreign branches in the decade prior to the crisis shows the very real risks that can arise when a branch is used to raise funds in the host country (in the United States, in dollars) through short-term wholesale borrowing, and then directs those funds out of the host country for loans or asset purchases by other parts of the bank.