There are hundreds of thousands of pre-owned paintings in the world and the vast majority are either by little known or totally unknown artists and quite a high proportion of these have unidentifiable signatures or no signature at all. Unfortunately, only a tiny percentage of second-hand art is by a famous or collectible artist.
Having said all that, many unsigned works do have a value. Many works in museums, for example, are unattributed. They earn their place through the quality of their workmanship. If your item is indeed a very old painting, and it is of good quality, and in good condition, it may be worth asking advice from an auction house with a dedicated art expert on the team. Email the auctioneer with your inquiry, and remember to include clear photos of the front and back of your painting together with close-ups of any labels or other distinguishing marks.