This is a bare-bones issue and requirements are subject to change:
Last read location should be stored using localStorage.
When a user visits a work or chapter, ask them "Do you want to have your read position saved locally on your device? Your location will not be stored centrally, this preference can be change by accessing local preferences in the page footer" if we've never asked them before. Their preference will apply to all works/chapters visited from the same browser.
If they have agreed to have the read location saved, jump to the read location.
Works in single page mode and in chapter-by-chapter mode should have separate read locations.
When a user finishes reading a work or chapter, the last read location should be removed.
As a user scrolls on a work/chapter, the last read location should be re-saved.
There should be a local preferences page, linked in the Archive's footer.
This page should detect and warn if localStorage is not supported by the browser.
This page should allow users to enable or disable saving last read location.
There should be a page listing which works/chapters currently have last read locations saved locally. Users will have options to resume reading works/chapters, delete last read locations for works/chapters, and as a stretch goal, export/import last read locations.