How can non-backed cryptocurrencies be stable (like by algorithm)
It's entirely possible, but no one would invest in such a coin because the return on investment would be predictable and low, and the value itself would be subject to manipulation by the creator. You are basically describing how a Federal Reserve works, and a cryptocurrency that acted like a Fed is useless. 

Also, nothing in the blockchain indicates price, so you'd have to source price from an exchange. Each exchange price varies, so it's arbitrary and gameable which exchange is picked.