Fossil records of vertebrate integuments are relatively common in both rocks, as compressions, and amber, as inclusions. The integument remains, mainly the Mesozoic ones, are of great interest due to the panoply of palaeobiological information they can provide. We describe two Spanish Cretaceous amber pieces that are of taphonomic importance, one bearing avian dinosaur feather remains and the other, mammalian hair. The preserved feather remains originated from an avian dinosaur resting in contact with a stalactite-shaped resin emission for the time it took for the fresh resin to harden. The second piece shows three hair strands recorded on a surface of desiccation, with the characteristic scale pattern exceptionally well preserved and the strands aligned together, which can be considered the record of a tuft. These assemblages were recorded through a rare biostratinomic process we call "pull off vestiture" that is different from the typical resin entrapment and embedding of organisms and biological remains, and unique to resins. The peculiarity of this process is supported by actualistic observations using sticky traps in Madagascar. Lastly, we reinterpret some exceptional records from the literature in the light of that process, thus bringing new insight to the taphonomic and palaeoecological understanding of the circumstances of their origins.