The guy was most definitely asleep. And the cord from the purse was wrapped around his neck and the killer put themselves in a good position behind and probably above him so he couldn’t do anything to defend himself.
If it was a robbery no one would go through that amount of trouble.
The police find her story with holes. It looks bad for her.
Another story in this case stated that the guy was passed out drunk and that they had a very jealous relationship with each other.