It seems that certain home router firmware is designed to work with Dynamic DNS services (e.g. noip & dyndns) to serve a subdomain from a server behind a consumer ISP. On a similar note, are there any dynamic dns services that will work with a shared web hosting account?
Example
For instance, Dreamhost has an API that can retrieve a domain name's IP address. In theory, the dynamic DNS service would periodically make a request to the Dreamhost API for the website's IP address. If the IP address on Dreamhost changes, the DNS host would automatically make the necessary changes to the zone file for that website as soon as it notices a discrepancy.
Why?
In the past, I had paid for a static IP address on a shared host, my domain name was registered at GoDaddy and the nameserver was set to EveryDNS. Due to catastrophic hardware failure at the shared host, my site was moved and the IP address changed.
In the example setup above, the DNS records would have automatically updated. Instead, I had to manually update my A record.
Question Summary
Is there a Dynamic DNS hosting service and shared web host that will allow this?
Is the solution proposed in the above example viable?
Bonus (at the risk of exposing my ignorance on this subject): are there any other ways, outside of DNS, to detect the IP address for a website? Perhaps a script in your shared hosting directory could detect an IP change and notify the DNS host?
Thanks in advance!