What is the ruling on one who performed tawaf and sa'i not being in a state of wudu after their wudu was nullified during sa'i and tawaf al-wada' and they were unable to renew it?

Sa'y between Safa and Marwa is valid without ritual purity because purity is not a condition for it. As for the Farewell circumambulation (Tawaf al-Wada'), it is not valid due to the condition of ritual purity for it. You must repeat it as long as you are in Mecca; otherwise, you owe a sacrifice (dam) to be slaughtered in Mecca for the poor if you have already traveled.