After a prisoner is executed in prison then the family members if there are any will be contacted to take the body of the executed prisoner if they want too or they are available.
If there are no family members to take the body of the prisoner who was executed then they will usually bury the prisoner in a graveyard on the prison grounds.
Or the prisoner may be cremated and the ashes spread somewhere or they can mail the ashes to family if anyone is available.
Some prisons have other inmates help do a funeral on prison grounds for the executed prisoner or for prisoners who die while in prison.