Can my website be put into a file that someone can use to re-establish it after i die?

My website has been on the web for about ten years now. After I learned to do everything right, it's been completely trouble-free.

     I don't write any code. I have always used EasyWebEditor, which changes PDF into code for me, and lays the site out the way I select.

     I want to perpetuate the site after I am no longer here, and I cannot find a webhost willing to talk about longer than five years or so.

     It occurs to me that there must be a way to put the site into a conventional form of the type that people who code use, and that if I had that, I could put it on the site and offer it as a download to anyone interested in perpetuating it should it disappear.

     It's basically one page, with about 50 blue-line clicks that lead to sub-pages. Sometimes there is a trail of blue-line clicks leading to other sub-pages. There are jpegs.

      Can this be done? Who can do it? What would be a fair price?