Can you refuse a job offer while on unemployment? Sometimes, under strict guidelines Florida unemployment will require job searching again, One local mother says she doesn't have many options. and last updated 2021-05-14 18:03:02-04 TAMPA, Fla â If you want to keep your unemployment benefits, youâre not only going to have to put together a resume but send it out every week. âItâs been difficult for me because I do want to work,â said Michelle Hernandez. âBut, being eight months pregnant, having a child, and then daycare being so expensive I was like what can I do?â Itâs a legitimate question many parents have asked.