Nice suggestions, thanks! 
I agree.
Cardboard by itself isn't entirely trustworthy (all bets are off should I fall on the blade at an unlucky angle). But reinforced with other materials as suggested, it should be a considerably more robust.
You mean just cardboard and tape isn't trustworthy? 
I've made a sheath the way I described above , 
with just one wrap (three blade widths) 
of brown cardboard from a crackers box
about 1/32inch(~.8mm) thick 
I stabbed the sheathed knife into the floor several times,
it didn't poke through, 
I stabbed at an angle, no pokes,
I pushed the edge into a table, edge didn't cut sheath
How do I get it to fail?
The only way I think its possible, aside from slicing it intentionally, is impact with hammer against anvil
cardboard from tetra-pack box of milk ought to be waterproof