Your mention of DNS gives a clue to how this works.

Presumably you expect clients to host DNS with you, then you can proxy to the real site, or the static site in case of failure? Or is there more to it than that, with DNS-updates on failure?

Just small correction here,

> When your website goes down, we take care of your customers and make sure they don’t run to your competition.

I think the last word should be "competitor" not "competition"