Yes, virus stay on the dead bodies but the question is for how long. There is another thread on this. Back in the days of SARS, dead bodies were zipped up in body bags and taken straight from the morgue to the crematorium by people in full PPE gear - body suit, full face and neck protection.
Trailers are contaminated but again for how long. Since they found COVID-19 virus in cruise ship cabin for 17 days, I would say air the trailers in the sun for at least 17 days after the last body is removed.