If sponsoring someone who has overstay visa can they get a work visa?

How are you sponsoring them for a work visa?  Normally, someone has engaged in employment without work authorization for 180 days or more is disqualified from being able to get a visa or green card in the U.S.  If the visitor visa overstay on the entry card is more than one year, then they will be barred from returning for 10 years if they leave the U.S. for visa processing. If you filed an application with the U.S. Department of Labor and/or the U.S.C.I.S., then you should consult with an attorney.  Perhaps, someone should review what has happened to date and provide you with legal advice.  Our office, like most others, provides Zoom Conference video calls.