Pesachim 21a - Is one in violation of owning chometz that they don't know exists?

Generally speaking we assume that בל יראה ובל ימצא have nothing to do with actually seeing or finding chometz. The braisa on 5b makes it clear that hiding chometz so that one doesn't see it, accomplishes nothing to avoid the issurim. However, in that context we only include in the issurim chometz that one is fully aware of. There is a big machlokes Rishonim (Tosafos 21a and Rosh 6b) whether one is in violation of בל יראה ובל ימצא on chometz that they are completely unaware of, even without being mevatel it.

The gemara on 21a says that if we were only told that one can leave chometz in a place where there is a חיה, that is because a wild animal has a tendency to hide the chometz, but a more domesticated animal that will not hide the chometz, rather leave it out in the open causing the violation of בל יראה ובל ימצא, we would think that it is forbidden to feed them prior to pesach. The gemara seems strange. How does the wild animal hiding the chometz help the owner avoid בל יראה ובל ימצא? Tosafos derives from here that any chometz which exists in a hidden place that the owner is unaware of is not subject to the issur of בל יראה ובל ימצא. Unlike בל יטמין which is assur because the owner knows where it is, here the owner doesn't know where it is. Based on this, Tosafos explains the question of the gemara 6b, why must one be mevatel on the night before erev pesach, just be mevatel when you find it? The gemara answers you may find it after it already became issur when it is already too late to be mevatel. Tosafos understands that the gemara knew all along that we were speaking about finding it once it has already become assur, yet being mevatel at the point when you find it would be sufficient because until you find it there is no violation and when you find it you will immediately be mevatel. To which the gemara answers that after the chometz becomes assur bitul is not longer a possibility.

However, the Rosh 6b explains that by the Torah writing לא יראה rather than  לא תראה it implies that one cannot have chometz in any area that it is fit to be seen, even if now it is not known about and not seen. Therefore, if a person was lax on bedikas chometz and found chometz on Pesach that they were not mevatel, according to the Rosh they were in violation of בל יראה ובל ימצא the entire time. Whereas Tosafos will hold that they were not in violation until they find it since they didn't know about it, and even when they find it they are not in violation so long as they are busy trying to destroy it (as tosafos writes 29b d.h. rav ashi).

According to the Rosh, the gemara 6b which suggests to be mevatel when you find it was assuming that one would find it prior to the z'man issur when bitul was still possible, to which the gemara is mechadesh that we are concerned that he will find it after the z'man issur. Therefore, without being mevatel in advance he will be in violation from the moment of the z'man issur even though he has not idea that it even exists.