Theorically what will happen to CBSA records if entering Canada by plane but leave into US by foot without passing a legal crossing?
Is this possible to walk in US without being caught and reported?
Yes. Easily. Not without some risk.
@GandiBaat covered much of what is relevant, even referencing the Haskell Library and Opera House in both Stanstead, Quebec and in Derby Line, Vermont. Been there. Parked on the wrong side of the border but, after being advised by staff in the library, quickly relocated our vehicle to park on the street on the Canadian side of the border. See
https://haskellopera.com/tours/
Been many years since I was last in that neighbourhood, so I am not sure the streets are still open to vehicular traffic crossing the border (like I did), or whether more prominent border markings have been installed. When I drove across the border there I did not even see the marker. It was not until I relocated our car and when walking back to the U.S. side to go in the library I noticed it, just a three foot high pole and not at all conspicuous.
As
@GandiBaat referenced, there are scores and scores of locations where individuals can quite easily cross the border without properly making an application to enter the other country. Whether or not they are apprehended depends on various factors, not the least of which is the extent to which the traveler is trying to cross the border undetected. As I recently mentioned, another commonly used unregulated border crossing location, Roxham Road, has been in the news a lot lately, but most of those crossing the border there these days are individuals coming to Canada who plan to make a claim for refugee status from within Canada and thus are crossing the border openly and planning on being arrested.
Unregulated border crossings are common. Unregulated border crossings are far more common than typically acknowledged by those who advocate IRCC should totally rely on the entry and exit records captured by CBSA.
There are other ways that exits from and entries into Canada are not captured in CBSA records.
Obviously, no record is captured unless the individual's identity is entered into the system, which requires either an electronic/digital scan of identification or a manual entry of the information. Omissions or failures are way less common these days but still happen.
Travelers sometimes have alternative travel documents, and these in turn sometimes do not link to the same client identification number. Here too this is far less common of late, but not that long ago it was not uncommon for some individuals to actually have two different Canadian immigration client IDs, and the border crossing information captured by CBSA would depend on which travel document was being used. It appears that this is something of a loophole some travelers, typically with the assistance of crooked consultants, still try to exploit.
Impact:
No mystery. If someone enters Canada without CBSA capturing a record of the entry, CBSA does not have a record of that entry. If someone exits Canada into the U.S. in a manner that is not captured by CBSA or by U.S. authorities, likewise CBSA will not have a record of that individual's exit from Canada.
While IRCC and CBSA rely on the accuracy of the CBSA travel history, they do not rely on it to be complete.