Can immigration/passport officers check for past flight information of a passenger?

I don't know exactly what border guards can see when checking your passport in each country of the Schengen area but as far as I know, there is no Schengen-wide database of entry and exits and no comprehensive records of all flights leaving and entering the area. Some countries (including Spain) do require carriers to provide information about their passengers and might therefore have more detailed records of your coming and goings but this information is not shared among all Schengen countries (at least for law enforcement or border protection purposes, I have absolutely no idea about intelligence services) so if you enter and leave through different countries, it would not be readily available to the border guards.

The main thing border guards can use to check whether you haven't overstayed are the entry and exit stamps in your passport. Those are defined in details in the relevant EU regulation. Importantly, if one stamp is missing, the authorities “may presume that the holder does not fulfil, or no longer fulfils, the conditions of duration of stay applicable within the Member State concerned” (article 11 of the Schengen Borders code). What this means is that they don't need to prove you overstayed, you need to prove you did not.

Note that a cancelled flight does not per se free you from the rules on the duration of stay in the Schengen area or entitle you to a visa extension. Generally speaking, you have to make sure you don't stay too long, possibly by planning a buffer of one or two days at the end of your stay or by making alternative plans and booking an expensive ticket if needed.

If leaving becomes impossible for “serious personal reasons” (say you are in a hospital bed), you have to arrange for an extension of your Schengen visa or a national visa as applicable. Convenience is typically not enough to obtain such an extension and you can't just ignore the regulations and then prevail yourself of a cancellation later on. Even genuine personal reasons will not always be deemed serious enough to warrant an exception.

Of course it's still possible to get lucky and to find border guards who don't check too carefully or accept your explanations and turn a blind eye, especially if it's only for one day. But you can't count on them knowing about the cancellation or even having any interest in your story. At the end of the day, if you have stayed too long, you have broken the rules and they can punish you for it.