Tying with wrap
Roll the sheet lengthways into a band, take three wide turns round both limbs, and tuck the end back under the last turn.
How it is done
A bedsheet rolled tight along its length becomes a wide soft band that holds surprisingly well and cannot cut in anywhere — the width does all of the work. Three broad turns round the pair, then feed the end back under the last turn and pull it flat. It will never be as secure as rope and is not meant to be; this is the material for holding somebody who has already agreed to stay held.
What goes wrong with this one
Wrapping traps heat far faster than people expect — heat is the real risk here rather than escape, so the room gets cooled first and it comes off at the first complaint of being too warm.