I have an improvement to a product. Let's call the improvement "A" and the product "B". Improvement A is not novel, product B is not novel. The way A & B are combined is novel. I want to patent combining A + B. Can someone sell my improvement to users of the product B? I realize that anyone who uses A+B is infringing the patent, but suing end users is rarely good for business.
If A applied to B is novel and not obvious then you might get a patent for the combination of A and B configured a specific way. Or a method of operation that only happens when A is attached to B.
Someone selling A alone would not infringe but, as you say, the end user who attaches them together would be a direct infringer. A company that sold A specifically for being attached to B might be an indirect infringer. See this article. They might do this by their advertising or instructions that came with the A they sold.
You need to prove that at least one person actually infringed as part of going after a big indirect infringer but it is the big infringer selling A for the purpose of using it with B that you would target.
edit - I just saw this in a previous answer I gave. It has limited applicability if A is already in commerce as a separate product -
see 35 US 271 (b)
c) Whoever offers to sell or sells within the >United States or imports into the United States a component of a patented machine, manufacture, combination or composition, or a material or apparatus for use in practicing a patented process, constituting a material part of the invention, knowing the same to be especially made or especially adapted for use in an infringement of such patent, and not a staple article or commodity of commerce suitable for substantial noninfringing use, shall be liable as a contributory infringer.