We address certain challenges related to the analysis of moving boundary problems of parabolic-hyperbolic type. In particular, we focus on a fluid-structure interaction problem between the flow of an incompressible, viscous fluid and a multi-layered poroelastic structure, which behaves as a compressible material. The coupled problem is described by the time dependent Stokes equations, which are coupled to the Biot equations over a poroelastic plate serving as an interface between the free fluid flow and the poroelastic structure. This problem was motivated by the design of a first bioartificial pancreas without the need for immunosuppressant therapy. We will show a recent constructive existence proof for a weak solution to this problem, and a (weak-strong) uniqueness result. This is one of only a handful of well-posedness results in the area of fluid-poroelastic structure interaction problems. The mathematical reasons for this will be discussed, and the impact on the design of a bioartificial pancreas will be shown.