While the scope of "Full" in "Full stack developer" is a subject of open debate, There are multiple "perks" of being open to exploring multiple parts of the stack.
First and foremost ability to handle issues and integration across the stack allows you to utilize your time better and alleviates having to go back and forth between team members. For example, in a typical web development context having basic understanding of CSS can allow backend developers to quickly fix visual regressions. Having exposure to command line and shell programming can often help in resolving deployment issues.
Being involved in multiple parts of the stack makes you more valuable from the perspective of an employer because it is common for software projects to eventually become overstaffed or understaffed during their course of evolution. Being flexible makes it easier for the project overseers to systematically distribute workforce elastically as per changing requirements.
It also implicitly becomes evident that you are open to exploring new and emergent technologies because you already have a proven track record of working across languages/frameworks/ecosystems. This contributes towards your value from the perspective of an employer.