Numerical simulations predict the existence of old Tidal Dwarf Galaxies (TDGs) that would have survived several Gyr after the collision lying at their origin. Such survivors, which would by now have become independent relaxed galaxies, would be ideal laboratories, if nearby enough, to tackle a number of topical issues, including the distribution of Dark Matter in and around galaxies. However finding old dwarf galaxies with a confirmed tidal origin is an observational challenge. A dwarf galaxy in the Virgo Cluster, VCC 2062, exhibits several unusual properties that are typical of a galaxy made out of recycled material. We discuss whether it may indeed be a TDG. We analysed multi-wavelength observations of VCC 2062, including an IRAM CO map, an optical spectrum of its HII regions, GALEX ultraviolet and archival broad-band and narrow-band optical images as well as a VLA HI datacube, originally obtained as part of the VIVA project. VCC 2062 appears to be the optical, low surface brightness counterpart of a kinematically detached, rotating condensation that formed within an HI tail apparently physically linked to the disturbed galaxy NGC 4694. In contrast to its faint optical luminosity, VCC 2062 is characterised by strong CO emission and a high oxygen abundance more typical of spiral disks. Its dynamical mass however, is that of a dwarf galaxy. VCC 2062 was most likely formed within a pre-enriched gaseous structure expelled from a larger galaxy as a result of a tidal interaction. The natural provider for the gaseous tail is NGC 4694 or rather a former companion which subsequently has been accreted by the massive galaxy. According to that scenario, VCC 2062 has been formed by a past tidal encounter. Since its parent galaxies have most probably already totally merged, it qualifies as an old TDG.