I have read extensively about this issue and found out that this is not really true. Without having agreements in place and consent from applicants this will not happen. European countries do have share information among each other but not to other countries. In case of asylum claims they would know a prior claim was filed in another member state by comparing fingerprints in the EURODAC database but they would not know the details of the claim. This info is deleted after 10 years.
Having said that, I would still advise anyone to answer truthfully to all questions asked and to respect other countries laws even if they don't agree with, or else they can choose to immigrate elsewhere. But I wouldn't mislead people into believing their previously disclosed information is not in their control and is being given out to 3rd parties without their consent. I believe that when applicants are given assurances their information is kept protected and safeguarded they are more likely to be truthful about their circumstances.
Few things:
1. Would they try to apply for permanent residency in Canada, they will give the consent for their personal information to be disclosed. (fully in their control, as they can choose not to immigrate to Canada and then nobody will search for their past).
All it takes after that is contact their allies and search after personal information for that person
2. Such claim does leave a bit more traces there. We are talking about fingerprints that are going nowhere (for what if purpose later on) - one thing is the EU database and the other thing is the local police of the affected country, that can use the local law; we are also speaking about other organizations that are dealing with social assistance. And of course about commercial carriers.
So if ever such question would not be answered truthfully, traces of that person being in Europe can be found. So the moment they would answer no, and something would be found, it would lead to misinterpretation. And if ever they answer yes, they need to disclose the basic situation. Otherwise the only thing would happen is an intensive search.