I always thought of it as a "left over" from the original St. James Infirmary song----the guy has syphillis so they give him salts of mercury to raise his body temperature to kill the spirochetes; then they wrap him in linen to increase the rise in body temperature.

After that, they put him on the roof of St. James to lie in the sunshine........and WHOOPS!! too much heat, so he cooks to death.

None of that really makes sense with the US cowboy version of Streets of Laredo but ballads often don't make sense when they are transferred from another culture.

The US cowboy version seems to be using the "white linen" as a shroud even though the boy isn't quite dead yet, but he is wrapped for burial and has Final Requests.......the 6 cowboys, maidens, etc. He KNOWS he is going to die and that he is wrapped for burial.

just my $0.02 worth