Can you give an example of a non-collateralized stablecoin? I am under the impression that all of them have some collateral backing the peg. Please correct me if I am wrong.

One minor correction:

The first thing is with collateral. When a collateral of 150% is set it means there is a 50% buffer before this asset loose it value. Ethereum or other tokens need to drop more than that for DAI to lose value.

A drop from 150% to 100% is a 33% drop in value of the token used as collateral not 50%: