My wife and I are retired. She will sponsor two broters form China using 864 income gudlines.

Will I be financially responsible for her sponsored family members?

What happens if she dies befor me while her brothers are still under her spojnsorship?

If you live in a community property state you will absolutely be responsible. It will be as if you signed the forms yourself. If she dies her estate (your estate) would carry the liability. Hide the pen!