EI is a different story. It's not the same as welfare from the government. We are paying Employment Insurance premiums so when we get unemployed, we will get something for a certain length of time. We get EI money because we have paid for the premiums.
For example, the sponsored person ran out of EI or never worked so walang EI na matatanggap. He can't asked for welfare from the government. It would be the job of the sponsor to support him. At least, that's what written on Family Class sponsorship. I'm not sure with the provincial nominee program but most likely, it would be similar.
As per CIC IMM1344 document for sponsorship:
UNDERTAKING BY SPONSORSHIP AND CO-SIGNER
I undertake to provide for the basic requirements of the sponsored person and his or her family members who accompany him or her to Canada, if they are not self-supporting. I promise to provide food, clothing, shelter, fuel, utilities, household supplies, personal requirements, and other goods and services, including dental care, eye care, and other health needs not provided by public health care. I understand that the money, goods or services provided by me must be sufficient for the sponsored people to live in Canada.
I promise that the sponsored person and his or her family members will not apply for social assistance.
I make these promises so that the sponsored person and his or her family members listed on this undertaking can be admitted to Canada as permanent residents.