It is recommended that a person end his night prayers with Witr, providing he knows he can pray it before Fajr. But if a person fears that he might over sleep until the Athan, it is permissible for him or her to pray Witr before going to bed and then if she wakes up before Fajr, she can pray as many Rak’ah as she wishes providing that she doesn’t perform Witr again.
And Allah knows best