Tex doesn't really allow you to do this, because it uses a 2-stage process. In the first stage paragraphs are divided into lines. In the second stage the lines are distributed over pages. Unfortunately, what you are asking for would require feedback from the second stage into the first stage.
Joseph Wright's suggestion will strongly encourage every full stop in the document to be at the end of a line, which will really mess up all your formatting, and it will still do nothing special to encourage the page break to fall at a full stop rather than one of the other lines of the paragraph.
Alternatively if you would do some Appendix-D-level trickery to implement a vertical-mode fullstoppenalty for lines ending in full stops, this would still be insufficient, because there is nothing that guarantees that any of the lines on the page will end with full stops, so you would still need to combine this trickery with something like Joseph's suggestion (with all of its caveats).
In order to get what you want, tex would have to do chapter-at-once optimization of line and page breaks, rather than the paragraph-at-once optimization that it gets from the Knuth-Plass algorithm. Chapter-at-once optimization is much more difficult because you have to solve a much harder problem (NP-complete in the presence of floats) that is not amenable to the dynamic-programming trick that lets Knuth-Plass be so efficient.