Curious if anyone has experimented with a dynamic DNS edge solution that allows you to literally have a "dynamic static IP" basically an actual public IP that d

Curious if anyone has experimented with a dynamic DNS edge solution that allows you to literally have a "dynamic static IP" basically an actual public IP that doesn't change that points to your dynamic IP? I had a client ask for this admittedly bone-headed config - ironically their DB server requires an IP not a domain name (which in most cases more than suffices for DyDNS).