First of all, I'm not sure if a D-brane can have a boundary? Naively, I can imagine under certain background potential(from NS B field or RR field), at the "D-brane boundary," the open strings could either stop moving or become closed strings propagating away into the bulk. Then, I'm wondering how would the energy and momentum transfer in the processes of an open string bouncing/leaving the boundary? Furthermore, if the boundary exists, one can even break a D-string into two or join two D-strings or extend a D-string by considering the dynamics with open strings! This seems to endanger the conservation of RR-charge?
On the other hand, I find it hard to overrule the D-brane boundary considering the fuzzy sphere, which is a well-known spherical D2-brane in IIA theory. What's wrong if we smash the sphere into a flat disk with circular boundary?