It is hard to find a single-family home in the Naples market around this price range, but if you do not mind living in a "starter home" that you would need to put some more $$ into, you can look to Naples Manor. This community is off Tamiami Trail on the East Trail west of Collier Blvd or 951. Most likely nothing around $50K but you could find a fixer upper around $70K and up. Good luck. Here is a link for your convenience.
You also have the option at looking at a condo form of ownership, where you will find condos priced under $100K.
Click on Naples Condos
Hope this helps. If you need additional help contact me through any listings on the site.
You can buy a trailer or small house in Collier County for the 50's however, you'd be looking at Immokalee the town. It about 26-40 east of Naples. Other than that, there isnt anything in naples itself in the way of a single family home for that price. Shoot me an email or call me and I can try to match you up to the right property in the right location. email@example.com