בבא בתרא עט:
"אבידה בביהכנ"ס"
The Mishnah in מעילה states if one is מקדיש a בור and later it gets filled with water, one is not מועיל if he uses the water. This is because the water wasn’t in the pit when he was מקדש it. תוס' says, we know that a חצר may be קונה for its owner, so here too, we should say הקדש that owns the pit, should be קונה the water through קנין חצר? תוס' explains that "חצר משום יד אתרבאי" and הקדש does not have a "יד" (The רשב"ם explains this way as well). The רמב"ן says that even if we would say that הקדש has the power of קנין חצר, there would still be no דין מעילה on any item they acquire through חצר, because the איסור of מעילה is not on items הקדש acquires ממילא, but only on items they are קונה through a אדם being מקנה it to them. The [או"ח קנד, אות כג'] מגן אברהם brings the אגודה who says based on our Gemara that הקדש is not קונה with חצר, if one finds a אבדה in a בית הכנסת he may keep it and we don’t say that the ביהכנ"ס was already קונה it through קנין חצר. The [ס' ר'] קצות החושן points out that this is only according to תוס' and the רשב"ם, but he learns that the רמב"ן holds הקדש is actually קונה there is just no דין מעילה, and thus accordingly, one would not be permitted to keep it. עיי"ש באריכות. The [קנד' ס"ק נט'] משנה ברורה brings the above מ"א and אגודה and adds – עיין חידושי רע"א. There, רע"א brings the above שיטת הרמב"ן and says (like the קצות) that according to this, there is no הכרח to say one may keep a אבידה found in ביהמ"ד. [יו"ד ח"ד ס' כג' אות יג'] ר' משה says one that finds an אבדה in a ביהכנ"ס or ביהמ"ד, if it doesn’t have a סימן, he may keep it, as is clear from the מגן אברהם בשם אגודה. It is interesting to point out, that ר' משה does not say to be חושש for the above שיטת הרמב"ן.
Many Meforshim ask [תוס' יו"ט מעילה פ"ג, ו'], even if you say the חצר of the ביהכנ"ס can’t be קונה because הקדש doesn’t have a יד, we also know that חצר works מטעם שליחות and that should work for הקדש? Maybe we can say [עיין בין הריחיים ב"מ יא.] according to the [ב"מ יב] רא"ש only a חצר המשתמרת works מטעם שליחות, but a חצר שאינה משתמרת only works through יד and therefore if it’s not משתמרת the בעל השדה would have to be standing near the חצר for it to be קונה. Also, the [גזלה,פי"ז,יא'] רמב"ם adds that when one wants his חצר שאינה משתמרת to be קונה for him, he must not only be "עומד בצד שדהו", but also verbalize and say "זכתה לי שדי". The גרי"ז, when accepting משלוח מנות, would wait for the נותן to put it on his table and then say "תקנה לי חצרי". Presumably, he considered his (open) house אינה משתמרת and was following the above רמב"ם that in this case one must also verbalize that he wants his חצר to be קונה for him. Maybe, so too, in our case of an אבדה in a shul where so many people come in and out, at least as many as in the house of the Brisker Rav, we would classify it as a חצר שאינה משתמרת,which would need ownership standing by and saying "זכתה לי שדי" for שליחות to work, which obviously can’t be done in our case, so subsequently חצר מטעם שליחות will not work in the ביהכנ"ס.