Here we study experimentally the behavior of liquid healing agents released in vascular core-shell nanofiber mats used in self-healing engineered materials. It is shown that wettability-driven spreading of liquid drops is accompanied by the imbibition into the nanofiber matrix, and its laws deviate from those known for spreading on an intact surface. We also explore coalescence of the released drops on nanofiber mats, in particular, coalescence of drops of resin monomer and cure important for self-healing. The coalescence process is also affected by the imbibition into the pores of an underlying nanofiber mat. A theoretical model is developed to account for the imbibition effect on drop coalescence.