Resigning employee put in writing they were calling out sick for their last 2 days because they start new job on Monday. Do we have to pay? [NY]

Me, HRG for a medium sized hospitality company. Employee gave written notice two weeks ago, with a final date of Monday, July 7th (first day of the fiscal week). They were scheduled Wednesday - Sunday 7.2 - 7.6. On Friday, an hour after their supervisor left, they texted the supervisor, saying they were leaving early because it wasn’t busy, and taking sick days on Saturday and Sunday because they start their new job on Monday (the 7th).

Can we prorate their final week of pay because they admitted in writing that it was not a valid use of sick time?

Company policy does not pay out sick time at separation, and doesn’t allow use of PTO while working out their notice, but does pay out remaining PTO. EE will get paid out 6 days.