I'm gonna post what I think would happen with attacks.
Regular moves (1 hit moves) like Stone Edge and what not will kill it.
Now with Multi-Hit moves.
Shedinja has only 1 HP. Sturdy will protect from a potential knock-out move leaving you at 1 HP.
Take Bullet Seed
1st seed hits!! Normally it would knock Shedinja out, but because of Sturdy, it leaves him with at least 1 HP, which just so happens to be full health. 2nd seed hits!! Process repeats, leaving you again surviving with full health. the process keeps repeating.
Only thing left is all that Mew :3 said.