See also, All About the Flag on the Casket.
There is a proper way to place the flag on the casket and we will look at purely the orientation and not how to place it or the procedures for changing it. Having said that, changing the orientation can be as simple as bunching up the flag and reorienting it in the proper direction, but that is if it is caught before the ceremony.
If the flag is oriented incorrectly and the honor guard is now standing in front of the next-of-kin (NOK), it’s time for Stars-Over-Stripes if it is upside down or backwards. No need to change anything if it is upside down and backwards.
Always place the flag with the canton over the left shoulder of the deceased. This display maintains the standards set forth in the Flag Code where the canton is always in the upper left. With the NOK seated in their proper palce, you can see how that looks.
In the above illustration, we see the standard set up of the flag-draped casket and the placement of the NOK. If at all possible, the NOK should not be located anywhere else.
Above, we have the four possibilities of draping the flag on the casket.
Note- the flag is ONLY draped on a casket (four sides), coffin (six sides, rarely used in the USA), and the transfer case. It is not draped on anything else, especially not the casket shipping container for commercial flights.