Q: If I had an idea for a new product but could not afford the cost of a patent , I sent myself a post office sealed

A: No. It will not help. Patents do not protect "ideas" - The only thing that is protected is the "structure" that allows the "idea" to work. The structure is the thing that is protected. What is subject to Patent Protection? it is a new structure that does something. There are many lawn sprinkler inventions. a new lawn sprinkler "structure" is subjection to Patent Protection. The Patent Examiner searches to see if the "identical" structure has already been invented or searches to see if existing inventions/patents "teach" the next inventor to do make an improvement. If the existing inventions/patents "teach" the making of the structure you are thinking of then your new structure is "Obvious" and will be rejected. Call a patent attorney.

A: Another answer - there is no protection where someone later, days or years later, invented the same "structure" as you described in you sealed letter. The USA used to be "first to invent" 2012-13, and then and before that "first to invent" person could control(but not with the mailed envelope.). But the law changed 2012-13 and it is now the "first to file" who controls. If you invent a "new structure" that does something and later, days or years later,another person invents the same "new structure" and ALSO file a patent application then that later inventor of the IDENTICAL "new structure gets the patent. The earlier inventor looses out.