Q) Is there any issue to purchase after Pesach chometz that was sold to a non-Jew before Pesach?
A) The Shulchan Aruch (OC 448:3) tells us that if one sold chometz to a non-Jew before Pesach, it is permitted [to eat after Pesach] even if the understanding is that the non-Jew will not consume the chometz; but will give it back to him after Pesach [as is often the case]. The only stipulation that the Shulchan Aruch makes is that the chometz must be sold or given over absolutely to the non-Jew – without any conditions or “strings attached” to the transaction. However, a matono al menas l’hachzir [a transaction where the giver stipulates that the recipient must return the item to him at a later stage] is not a valid transaction regarding the sale of chometz [and the chometz in such a situation will be forbidden after Pesach].
Therefore, it is a longstanding minhag to sell chometz before Pesach to a non-Jew and to buy it back after Pesach. Nevertheless, many refrain from selling “real” chometz before Pesach – if they are intending to buy it back from the non-Jew after Pesach. Similarly, many also refrain from purchasing from a Jew chometz that was sold to a non-Jew before Pesach (and bought back from the non-Jew after Pesach).
We find mention of both these stringencies in the practices of the Vilna Gaon (Ma’ase Rav, Items 180, 181) – that the Vilna Gaon would not sell chometz to a non-Jew before Pesach unless he intended not to buy the chometz back after Pesach. Additionally, he would not purchase after Pesach chometz that had been sold to a non-Jew before Pesach.
It should be emphasized that the practice of not purchasing chometz that was sold to a non-Jew before Pesach is a stringency; because according to the Shulchan Aruch and other Poskim it is fully legitimate to sell chometz to a non-Jew before Pesach and to buy it back from the non-Jew after Pesach.