One does not tie a "permanent" knot on the tachrichim (burial clothes) in order to show that the death is not permanent. That is, the person will get up at techiyas hameisim (resurrection of the dead) after the mashiach comes. Additionally, the knots are this way so as not to hinder the dissolution of the tachrichim with the body. The chevra kadisha that I did taharas for explained the twists as making sure that they will not come apart immediately. We just twisted the strings together tightly and then used the tension of the twists to curl them down. We did not use any knots (even bows or slip knots).
Permanent, double knots are not used at all, even to tie the thread
when stitching the shrouds. Everything is either twisted together or
tied with a bow tie / slip knot, which is a temporary knot, to show
that the burial is "temporary" until the resurrection of the dead.
The tachrichim, or shrouds are fashioned after the garments that the
high priest wore in the temple on Yom Kippur. They are white, made of
linen, and hand-sewn with no knots so that they will disintegrate
easily. They are made without hems, to signify their impermanence, and
with no pockets, because you can take no worldly goods with you into
the afterlife. Everyone: rich or poor, young or old, are buried in the
same garments. The caskets are also uniform, made out of wood, with no