Lost and Found - A gallery of overlooked optical nuclear transients from the ZTF archive

Tidal disruption events (TDEs) correspond to the destruction of a star by the tidal forces around a black hole, leading to outbursts which can last from months to years. These transients are rare, and increasing the current sample is paramount to understand them. As part of the Fink alert broker, we have developed an early detection system for TDEs for the Zwicky Transient Facility (ZTF) data. In this paper, we report on the optical transients we found either during the development of this tool, or when applying the classifier to the existing archive. We use this sample to anticipate what improvements to the TDE detection systems will need to be implemented for future surveys. For all the transients, we present optical and infrared archival photometry from ZTF, WISE, and Catalina, and assess the previous nuclear activity of the host. We fit the ZTF lightcurves with both a phenomenological and a physically-motivated model. We report on a total of 19 optical nuclear transients, out of which nine are in passive galaxies, eight in active galaxies, and two for which the activity of the host is uncertain. Two transients are newly discovered repeated TDE candidates, and we compare them to the current sample of repeated optical nuclear transients. One transient is exceptionally long-lived (over 5 years), in an until-now passive galaxy. Three of the TDE-like flares in active galaxies have absolute g-band magnitudes brighter than -24, making them new Extreme Nuclear Transient (ENT) candidates. One seemingly repeated object was revealed to be two independent supernovae in the same galaxy. This sample shows both the potential of our detection system for future discovery, and the relevance of archival searches to reveal overlooked transients. It also raises several points of concern and avenues of improvement for current and future classifiers.