the subject and the verb have to agree. The subject and the object do not. John does not like eggs. I do not like hookers. He or she does not have any hooker eggs. Someone is in the kitchen with Dinah's nine sisters. In this case, the object itself isnt even plural, its a singular described with a plural posessive. "Their hand" is just one hand. Just like the poeples' champion is just one champion.

Jack and jill have a hand. Someone is playing against them. He does not know what their hand is.

Granted, this is not the message one would typically be attempting to convey. However, the sentence is not grammatically incorrect in and of itself. Presented without context (which is is) as merely a showcase of the words there and their, there's nothing there. It just doesn't mean what most people probably think it does.