My sister lived with her boyfriend who died a few weeks ago and left several credit card balances. She keeps getting collection calls telling her she has to pay them off, but she did not apply for any of these herself. Is she liable for credit card?

No. Just have her return the mail unopened, marked deceased. As long as she is not a co-signer on the account, she is not liable for them.

If the boyfriend left an estate, then only the estate is responsible and the executor of the estate has to handle it.