Chametz Concerns for Non-Jewish Employees During Pesach

Rabbi, as the CEO of a company employing numerous non-Jewish workers, I am presented with a concern regarding the upcoming Pesach. Given that my employees frequently bring their lunch from home, which may include chametz, should I be worried about the presence of chametz in the workplace during Pesach? What guidance does Halacha provide in this scenario?

Thank you for your question.
The question you raised is an important one and it's good you are asking it before Passover since this needs planning before Yomtov and clear instructions.
The Shulchan Aruch, Orach Chaim, Laws of Pesach, 448, discusses a relevant case about Chametz (leavened bread) during Pesach (Passover). It states:
"If a non-Jew brings his own Chametz into the home of a Jew, the Jewish homeowner is not obligated to remove it. Despite the Jewish individual being aware of the non-Jew's Chametz, no infringement occurs."
Further clarification is provided by the Mishnah Berurah, which elucidates that the prohibition against possessing Chametz applies solely to one's personal ownership. As the Chametz in question is owned by a non-Jew and constitutes his private property, the Jewish individual does not violate this prohibition.
However, a concern arises since the worker may inadvertently leave behind crumbs or other residues, whether on the desk, around the table, or in the trash can.
The principle "חצר של אדם קונה" implies that ownerless objects entering someone's property automatically become their possession. This suggests that any chametz left in an office could potentially be acquired by the office's owner. However, this automatic acquisition does not apply if the recipient has no intention of claiming ownership. Therefore, in cases of chametz inadvertently left on the property, the owner does not acquire it.
I would like to illustrate this by an incident involving my in-laws in Belgium. After diligently cleaning their home for Pesach and celebrating the Seder, they were shocked to find a packet of crackers posted to their house the next morning. A non-Jewish Belgian cracker company had distributed these as part of a promotional campaign, mailing them to numerous homes, the Rav of Antwerp explained that such cases, where chametz is received unintentionally during Pesach, do not result in automatic ownership.
However, the Mishna Berurah Siman 440 18. Writes as follows
משנה ברורה סימן תמ ס"ק יח
“אבל בשעה שאינו אוכל מותר לו להניח לעכו"ם לאכול על שלחנו רק שיזהר הישראל לנקות השלחן ולהדיחו יפה אחר אכילת העכו"ם שלא ישארו שם פרורין מחמצו וכן צריך ליזהר כשילך העכו"ם מביתו שיטול כל חמצו ולא ישתייר ממנו מאומה”:
“that it is permitted for one to allow a non-Jew to eat at his table, provided that the Jew is careful to clean the table and rinse it well after the non-Jew's meal so that no crumbs of chametz remain. Similarly, he must be careful when the non-Jew leaves his home to take all the chametz with him so that none of it remains behind”.
The rationale for this is not based on concerns of ownership acquisition of the chametz, as we explained, but rather it is a rabbinical prohibition. The law seeks to prevent a situation where chametz might inadvertently be eaten, hence the requirement for the non-Jew not to leave any chametz behind.
According to this, since it is almost not impossible to keep track of the crumbs and leftovers that the worker will leave behind, one should offer a stipend in exchange for the worker not bringing his lunch over Passover, and ensure a “no food on-premises” policy he will then be able to buy to buy whatever he wants.
It is important to note, that one should not give the worker vouchers of a specific takeaway since that is considered doing business with chamets, rather one should give him money and say “buy whatever you want”, and then even if he ends up buying chamets that would be his choice (Mishna Bearura siman 450,17.
Wishing you much success and a happy and joyous Passover.

Shulchan Aruch, Orach Chaim, Laws of Pesach, 448
Mishnah Berurah, Siman 440, Se'if Katan 18
Mishnah Berurah, Siman 450, Se'if Katan 17