Frost formation is a major problem affecting a variety of industries including transportation, power generation, construction, and agriculture. Currently used active chemical, thermal, and mechanical techniques of ice removal are time-consuming and costly. The use of nanotextured coatings infused with perfluorinated oil has recently been proposed as a simple passive antifrosting and anti-icing method. However, we demonstrate that the process of freezing subcooled condensate and frost formation on such lubricant-impregnated surfaces is accompanied by the migration of the lubricant from the wetting ridge and from within the textured substrate to the surface of frozen droplets. For practical applications, this mechanism can comprise the self-healing and frost-repelling characteristics of lubricant impregnated-surfaces, regardless of the underlying substrate's topography. Thus, further research is necessary to develop liquid-texture pairs that will provide a sustainable frost suppression method.