Emirates's responsibility ends at JFK and for the travel onwards it is the passenger's responsibility. If the person misconnects in Dubia and will miss their onward flight and EK does rebook the passenger , I would advise phoning the airline which the US domestic flight is booked with and changing it and paying change fee/fare difference ; if has travel insurance then see if this can be claimed

If they just no-show, then the whole fare would be lost