While unemployment, itself, is not an automatic reason for exemption from the healthcare penalty, it may result in your annual income bring so low that you can be exempt.
Unemployment can also lead to other hardships, such as homelessness, threat of eviction or foreclosure, or disconnection of utilities, that are causes for exemption from the penalty.
Please refer to Are
You Exempt From Health Care Coverage? to find out if you qualify for an exemption.