Dynamically typed databases are often used in the NoSQL space, such as MongoDB, where data structures within collections can be flexible and variable. This approach can bring benefits to programming languages that also use dynamic typing, allowing for more flexibility and consistency in data storage. On the other hand, statically typed programming languages like Java may lose some of the power of static typing when used with dynamically typed databases, as type matching errors are only reported at runtime. However, relational databases could potentially be designed with dynamic typing, where tables can have flexible columns and values, offering a compromise between flexibility and consistency in data storage.