The internet is crawling with sites that are similar to what you mention, and they are just as a much of a problem for us, the providers, as they are for you.
First off, without doubt, some of the 'listings' for escorts in your area that you are looking at were probably fake right from the start. It is in these sites' best interests to appear to have a ton of traffic and information to offer. It is not uncommon for them to snag fake pics from somewhere, slap together a bogus ad, and pretend its real in order to make it look like they have alot more business than they really do.
Additionally, sites like this often cull through legitimate escort sites and simply create listings for escorts based on what they find. They don't bother to keep these ads updated, and don't bothter to contact the provider to ask her permission to post a link to her. In other words, it wasn't Suzie Q provider who created her own listing on the site, it was the website that created a listing for Suzie Q provider. She not only has no ability to control what is put there, but she in many cases, isn't even aware its been done.
My website allows me to keep track of where click throughs are coming from, and every day, I get clicks from various sources that I have never advertised on. Some of these sites I am able to track down, and at least verify that the information they provide about me is accurate. There are two sources though, that I've never been able to find the actual website where my ad is linked or listed. So someday, when I either change e-mail addys, or design a new webpage, or "go out of business" as you call it, these websites will point men toward a provider who can no longer be contacted. But its not my fault, and there isn't anything I or anyone else can do about it.
Stick with websites that are well known, and don't make you pay just to look at a list escorts. If they have to get money from YOU to run the site, they aren't getting money from the ladies - meaning the ladies don't necessarily have to be involved in creating their ads. When its free to you though, chances are we ladies are their revenue source, and when that is the case, you bet we know when there is an ad up, and what the ad says, and have control over the removal of the ad.