What happens when someone inadvertently enters the UK without a landing interview?

As a follow-on question to Which queue for a EU/non-EU couple travelling through UK Immigration Control together? for a question that arose in the commentary...

There may remain several routes into the UK where an arriving passenger may not be checked by an Immigration Officer. Some of these occur on Eurostar (or other rail/ferry) and others might occur at City Airport during certain times of the day, and others occur when a passenger is simply waved through controls (however unlikely this seems in the current era). Sometimes a walking route through an airport is not completely secured which leads to a land-side exit and passengers may inadvertently follow it.

Sometimes these 'loopholes' are discovered (proof that this has happened on Eurostar), and sometimes they are not, or go for a long time unnoticed.

This question acknowledges that arrivals through the Republic of Ireland are a separate case and are out of scope here (perhaps the topic of a future question). Similarly, arrivals at private airfields in the UK are out of scope. Also it's not appropriate in TSE to list current inward routes where controls fail because I cannot assume that everyone reading TSE is well-intended.

Of course it's easy to say that since it's UKVI's fault the person has no liability, but is this actually the case?

Assuming such routes exist and that the person is well-intended, what is their immigration status in the UK during the time they are present in the UK? Are they in violation of any particular rule? More importantly, is there a procedure so that the person can normalize their status? The corollary to this question is alternatively, should we trust that the possibility of this happening is too remote to consider realistically?

Credible/authoritative sources needed, court decisions and legislation (including Ministerial Statements) cites gladly welcomed. Other credible sources also welcomed.