I’m being furloughed due to the coronavirus, I got my residency through marriage 6 years ago but have not applied for citizenship as of yet so am still a conditional resident. If I applied for unemployment would my sponsor be financially responsible to pay back any benefit I received?
No, since unemployment is not any "welfare benefit."
No, your green card sponsor will not be liable if you collect unemployment. Unemployment is not a public benefit within the meaning of the public charge rule.
Unemployment is not a welfare benefit so nothing to worry about.
Please see https://www.avvo.com/legal-guides/ugc/public-charge-rule-is-expanded-how-does-this-affect-you-
Your question is for an immigration attorney and I forwarded it to them. You will get a response from them.