It's rather funny that ANY Canadian citizen can live in USA for up to half of year on a visitor status without bothering to obtain any visa like TN while the TN holder "loses lawful status" in US IMMEDIATELY after he loses job and "have to depart US IMMEDIATELY"
In the sense of helping a Canadian citizen enter US (not consider how long one can stay), A TN status (visa) is NOT an advantage, but a disadvantage (once you lose job).
However, one may state his status is changed to Visitor AUTOMATICALLY once he quits his job so he does not have to go out the states then reenter. Although this might not be allowed in US immigration law (or might be?), in practice, I don't think any people will bother to leave first and try reentry again, unless he is COWARD .They will definitely keep staying in US and look for another job. In addition, I really don't think there is any record that you lose your job. I seriously doubt if your former employer will report your status. Where and how to report? Even no such procedures in law, I think, although H1-B visa employer can and may do it. Unlike H1-B program where the employers file petition for you to immigration department, which means both the employer and US immigration dept. should record your crucial identifications for entry purpose, for the former TN employers to report you, however, the bottom line would be that they also have such kind of knowledge like your Canadian passport NO. or
TN visa NO. (if available) in hand. I know this is not the case. A simple employment letter let you get a TN status. They even don’t have any record in computer database for who and where is your employer. Thus US border officers won't question you next time when you enter US from Canada, so you have nothing to worry about.
The rules for Canadians to enter USA or how long he can stay in the states are sometimes ambiguous compared with other countries. At least the rules for Canadians are not strictly followed or are up to the individual border officer's mood how to explain and apply them. However the trend is it becomes stricter and stricter. Anyway, fortunately, in the world, who can enter USA MOST EASILY and who has the BIGGEST opportunity to stay long in USA compared with other country citizens? ----- Obviously Canadians.