Since this question was originally asked, Ancestry has not changed the policy quoted in Gene Golovchinsky's answer. Your tree remains intact, including the links to the content you've attached to your tree -- as long as the content is still on Ancestry.
However, if Ancestry removes content, you won't have access to a copy of that material anymore. Some examples:
- In 2009 Ancestry got into a legal dispute with L'Institut généalogique Drouin, the owners of the Drouin Collection, and the entire collection was removed from the website. See Whence the Drouin Collection? posted by The Ancestry Insider (Tuesday, September 1, 2009).
- Ancestry has re-published the collection known (as of this writing) as U.S. City Directories, 1822-1995. Here's a reference to a 2012 blog post when the new City Directory collection was in Beta: U.S. City Directories: One Database, a Billion Records, and a Lot of Answers (April 19, 2012). When this beta was complete, and the new collection was published, many of the links to the old collection of U.S. City Directories were left in place, and users with a subscription could still reach the images, but the information on the Record Page no longer displays. However, some of the oldest links to images saved in my Shoebox for later review have been broken. There is no information listed in the column Information on Record, and clicking on the link leads to an error page. Other pages show the city directory name and year, but no longer show the name of the individual I was looking for.
- In 2015 Ancestry decided to do a cleanup and removed or consolidated old databases. These were "text-only copies of books, city directories, and records that they have made available elsewhere with both text and images". See Ancestry Deletes Hundreds of Databases (The Ancestry Insider, Tuesday, October 13, 2015) which has links to discussion about the issue on other blogs. This deletion was especially annoying because Ancestry claimed "all of the material was available elsewhere" but did not release a list of what had been deleted, making it impossible for people to go out and find copies of what they needed to replace.
Whatever the reason Ancestry has for changing their collections, after being a subscriber for ten years, it's clear that the answer to the question "If my Ancestry.com subscription lapses will my links to premium data still be valid?" is It depends. or at least a qualified yes.
If Ancestry still has a valid license to the content, or they haven't ditched the database due to an underlying server-side problem, or they haven't discarded the database because it was small and "no one was using it", or they haven't lost it like the incident in 2016 where they lost a sizeable chunk of RootsWeb free pages, or changed it beyond all recognition as they did when they transitioned Genealogy.com to read-only status, then yes, your links will still lead to your content once your subscription resumes.
That's a lot of ifs, isn't it? This is why many of us do a screenshot, or print the record page to a file (which is all one can do for an index-only collection) and download the images to our own computers. There is no guarantee that any content you've saved to your trees or Shoebox will still be there between one login or the next, whether you are a subscriber, or not. In a comment on Oct 9 '12 at 22:56, Gene Golovchinsky
wrote, "Of course you can always save the images to your computer." That is sound advice for everyone, whether you keep your subscription all the time or let it lapse.
Edited to add material from comment:
Another potential pitfall is site re-organization. It's been a number of years since the last such change at Ancestry, but it can happen again. Maybe re-directs will be maintained. But security software sometimes baulks when confronted with them, and browsers can be set to prevent automatic forwarding. – bgwiehle
I think this is an excellent point. Site re-organization can happen at Ancestry itself (like the US City Directories 'beta'), or at the indexed site for all of Ancestry's indexes of off-site content (prefixed by Web: in the Card Catalog). With several of the Web: collections, such as public libraries with obituary indexes, or RootsWeb's Obituary Daily Times, Ancesty doesn't hold the index results, only a record page that says, in essence, 'we found this name in the index', and to get the complete data, the user has to re-run the search on the originating site.