That's for the money that's owed them from not paying the rent.

YouTube doesn't charge rent or other fees, and I'm not sure how they'd auction your digital copyrighted IP anyhow.

Yeah, but most places will put your storage unit into "default" for some time, usually 30 days, and make multiple attempts to contact you before auctioning your stuff. Generally speaking, in the U.S. most states have lien laws that dictate how and for how long a company must attempt to contact you before they can auction.

Youtube could do something similar, by providing you 30 days to download your content.

Those are mostly staged. In reality all they find is spiders and bits of cardboard boxes.

Don't know about where you live but where I do storage units are regulated and could not put a "burn your stuff" clause into the tenant contract even if they wanted to. It's a surprisingly highly regulated business.