Most likely it will be a matter of who will pay the most for the IPv4 addresses. Before the scenario you describe occurs, something else will happen.
ISPs will start using Carrier Grade NAT for all their new customers. Anybody who previously had a public IP from their ISP will lose it, if they ever need to switch to another ISP. This is going to result in a slow release of a small number of IPv4 addresses, and simultaneously reduce the quality of the service delivered to customers as a consequence.
ISPs who have been allowing customers to use multiple IPv4 addresses will start taking some of those away from the customers. That already happened to me once.
Should it happen that there are people who would like to deploy a server, but cannot get an IPv4 address due to cost or otherwise, there are still technical solutions which can be applied.
Frontends can be used to share a single IPv4 address between a large number of servers. I have developed one such frontend myself. I see no technical reason such a solution couldn't be scaled up to handle arbitrary number of sites with the number of IPv4 addresses being used remaining constant.
Others have suggested that hosting providers deploy reverse proxies on a few of the IPv4 addresses they have and let those provide connectivity to a large IPv6 only data center.