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The entire stringency of Gebrochts is only regarding eating it. It is however permitted to own Gebrochts even according to the stringent opinion. Accordingly, there is no issue with washing one’s floors that contain Matzah crumbs, even though one will come to bring them in contact with water, as one will not come to eat it.
 There is no known source for being stringent regarding owning [although Admur in Teshuvah 6 refers to “The prohibition of cooking the Kneidlach”, it refers to eating the cooked Knedilach as is evident throughout the letter which deals with a Biblcial prohibition even on Masheu Kemach, which does not apply with owning less than a Kezayis.] See Admur 463:2 [that even regarding roasted flour we are lenient regarding owning and benefit if cooked, and here this would seemingly apply even Lechatchila, as even the avoidance of eating is a stringency]; So is proven from the fact the Rebbe in the earlier years allowed feeding Gebrochts to children even initially, thus showing that we do not suspect for an owning prohibition. [See Toras Menachem 3:7] So is proven from Maaseh Rav that the Rebbe had Kneidlach prepared on Erev Yom Tov for the last day of Pesach. [Otzer Minhagei Chabad p. 255]; However, see Rav Levi Bistritzky in Kovetz Tiferes Limelech and Shut Ara Degalil who concludes that according to Admur that Gebrochts is a real worry of Chametz one may not make it at all on Pesach.
The reason: The prohibition of eating Chametz is more severe than owning. Thus, it is forbidden to eat even a small amount of Chametz, and eating Chametz carries the penalty of Kareis. Owning, however, is only Biblically prohibited by a Kezayis. There are many examples of cases in Hilchos Pesach in where we are stringent regarding eating and not regarding owning. For example, one may not eat Kitniyos although one may own it. There are many examples of cases brought in 442 and 447 of mixtures that may not be eaten but may be owned. Thus, unless one has explicitly received otherwise in his tradition, we cannot simply assume that the avoidance of Gebrochts includes not owning it over Pesach.