جَاءَ غُلَامُ زَيْدٍ
Ghulāmu has no tanwīn because it is the mudāf.
Zaydin retains kasratayn as a fully declinable mudāf ilayh.
Do not remove tanwīn from both nouns automatically. The mudāf specifically loses tanwīn; the complement follows its normal declension rules.