When the last day of Pesach falls on Friday can one eat chametz on Shabbat? If yes – what is the reason? The rabbi never made a kinyan with the goy to buy the chametz back and if we say that it is cancelled automatically since the goy “did not pay the balance” – that would mean one was over the issur of chametz b’pesach!
In this situation eating/drinking chametz on Shabbat is problematic.
One reason for this is that as you mention, no kinyan from the non-Jew can be made on Shabbat. The kinyan back from the non-Jew is only made after Shabbat, and therefore one must wait for motza’ei Shabbat before eating chametz.
Another possible reason for this is on account of muktzeh. The chametz is muktzeh on bein ha-shmashos as Shabbat comes in, and therefore possibly remains muktzeh for the duration of Pesach.
However, some are lenient on both counts: for the non-Jew’s chametz, because a clause is inserted into the contract with the non-Jew that permits eating the chametz, and for muktzeh because of the principle that muktzeh on account of the previous day’s prohibition does not extend into Shabbat (see Yecheveh Da’as 2:64, and see also comments below).
There is certainly no problem in eating kitniyot products that were kept at home during Pesach.