You will not be able to accomplish this using our nameservers since the nameserver itself is not aware of the name being used to request it so a call. This type of configuration would require it's own DNS server set up either with a wildcard domain "*" zone or by using another method to return a particular IP address for everything.

Setting up BIND on a droplet and creating a zone called * which directs to the IP address may do the trick.

webm3dia - I work for NameBright and we provide the nameserver software that does what you are talking about above. If your client was using us as a registrar, we have tools to make this automated and really simple. (free to use for all customers.) Essentially you set all domain names to be controlled at a "category" level. Any domains that move into that category automatically inherit the category level settings. In this case the domains would inherit our nameservers that would then point the DNS records to DigitalOcean's IP.