The answer is that yes, it is always possible. The history of how ancient works survive is filled with chance discoveries. Many many works we have today survive only by one known manuscript, and were one fire away from being lost forever. Virtually all of Cicero's courtroom speeches fall into this category, and 100% of Cicero's personal correspondence. "Private collections" in this context is probably misleading. I don't think there are very many "lost" works residing in dusty old castles, or else jealously hoarded by some rich Venetian family. If there are still undiscovered works, they are probably in the basements/archives of small churches in western Europe, especially France or the Rhineland. The Vatican archive almost certainly contains at least one yet-unknown find, but it may never be uncovered. It could be mislabeled, for instance. There are also palimpsests, texts which had been scraped away to make available their precious paper for psalters or church commentaries or whatever. We have a number of texts which have been "read" as palimpsests via modern imaging equipment. This is of course expensive, invasive, and potentially destructive. The institutions that control such texts are not always willing to subject their 12th century monk's musings on the nature of the trinity to such treatment in order to get a glimpse at the ancient texts which still faintly remains beneath. (Not all are as obvious or legible as this one). There are probably dozens, if not hundreds, of unread palimpsests out there.

Now about your text specifically. Any manuscript from the lost "epic cycle" is doubly unlikely. It SEEMS that these were already in decline even in the ancient world, and were already a rarity. Many might not have ever been written down at all, at least not as full-formed works, and plenty of scholars argue this point. They would suggest that the Homeric cycle is unique in that it was germinating at the right place and the right time to be recorded and later canonized into the Odyssey and Iliad as we have them today. There are lots of questions regarding this process. We have fragments of, for instance, the Theban cycle, but that is all (to my knowledge). The lost epics probably existed in their fullest forms during the Hellenistic period, and by late antiquity seem to have become scarce. This makes their survival to hinge on a desperate hope. Even texts which were common, like Homer, or Vergil, or Cicero, barely survive antiquity.