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As the UK has no exit checks, it depends on the circumstances of departure as to when any notice of action against you is given.
If you have come to the attention of the UK immigration authorities while still in the country, you will be issued paperwork at that time.
If you leave voluntarily, you will not be issued further paperwork during your departure (as UK immigration will only be aware of your departure after it occurs as airlines, ferry companies etc update them on passenger details).
If you leave involuntarily (ie you are detained and deported or removed), you will be issued final paperwork at that point.
If you have left voluntarily without coming to the attention of UK immigration while in the country, you may be given notice of subsequent action on your next interaction with the UK immigration system
If you have any doubt about your eligibility to enter the UK, then the suggestion is always to seek Entry Clearance before you attempt to travel to the UK or Ireland (as Ireland is part of the Common Travel Area, significant amounts of data is shared between these countries).