No, the solution in that scenario is "Spin up another VM, and talk to it over socket." That VM could be another unikernel server, or it could be vanilla Linux that you talk to over sshd, Fabric, Puppet, whatever.
It's important to understand the context behind the current unikernel hype: it assumes that you've embraced cloud providers (or at least run your own cloud on Xen or kvm), it assumes that you are building a distributed system, and it assumes your distributed system is built using standardized components. If 99% of software is various combinations of nginx, Node, Python, Ruby, the JVM, memcached, redis, PostGres, MySQL, and MongoDB, it can make sense to modify just those 10 applications to run on bare metal, cut Linux out of it entirely, realize gains of up to 10x in performance (based on the original MIT exokernel papers), and still present the same programming interface to application-level programmers.
Unikernels are not useful to people who just want to hack C on a single box, nor are they useful to giant companies like Google where all of their software is written in C++ with POSIX APIs. But they could save a lot of money for many mid-range businesses who currently host on AWS or GCE and write largely in high-level languages.