That’s not true. When my grandmother passed away, there was a Memorial Mass said specifically for her. There was a photo of her placed near the altar rail. The entire funeral liturgy was said, with funeral readings and funeral hymns, followed by the appropriate prayers that are always said at the end of a funeral when the priest blesses the body with incense. Afterward, there was a funeral luncheon. But there was no body, because her body was donated to cancer research. This is completely different from offering a regular Sunday Mass for the deceased. (Though this was done for her at several parishes as well.) To most outside observers, they attended my grandmother’s funeral. When we refer to it, we say, “at her funeral”. Technically, it wasn’t a funeral, it was a memorial Mass, but I’m sure that’s the sort of situation the OP is refering to. I don’t know if a priest would agree to this sort of arrangement so late in the game, but yes, they do take place.