While a US citizen sponsored spouse might not be ineligible to adjust for unauthorized employment. An LPR sponsored spouse would be ineligible. Further, while the sponsored spouse may not be ineligible for a green card. The employer may be penalized for employing without authorization. After the current EAD expires could take time off from work and wait for the new one. But, as you may have multiple EAD filings. Rather than be off work or work without authorization. We would recommend filing the C-08 EAD. It provides 180 days of employment authorization while the I-765 is pending adjudication to bridge the gap.