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אם היה משכירו לאחרים אפילו (מצא) בתוך הבית הרי אלו שלו: ואמאי ליזיל בתר בתרא

 The mishna teaches: If the homeowner would rent the house to others on a regular basis and there was a steady turnover of residents, even if one found lost items inside the house, these belong to him. The Gemara asks: And why do they belong to the finder? Let us follow the last renter and determine that he is the owner of the items.

מי לא תנן מעות שנמצאו לפני סוחרי בהמה לעולם מעשר בהר הבית חולין

Didn’t we learn in a mishna (Shekalim 7:2): With regard to money that was found before animal merchants in Jerusalem, it is always assumed to be money of the second tithe, as most of the animals purchased in Jerusalem were bought with second-tithe money. This halacha applies both during a Festival and throughout the year, as people would typically purchase animals for meat with their second-tithe money. If the money was found on the Temple Mount it is considered non-sacred money. This halacha applies even during a Festival, when people would come to Jerusalem with second-tithe money in hand, as it can be assumed that one who entered the Temple Mount had already spent that money and only non-sacred money is left in his possession.

Rashi writes: 

מעשר - שרוב בשר הנאכל בירושלים מעשר לפי שאין אדם שוהה בירושלים עד שיאכל כל מעשרותיו ונותן מעות מעשר לעניי העיר או לאוהביו יושבי העיר ורוב הוצאות מעשר לוקחין בהן בהמות לשלמים כדגמר שם שם מעשר משלמים במסכת מנחות (דף פב.):

Most of the meat eaten in ירושלים was from maaser sheni money because a person who comes to ירושלים would use up all of his maaser money [usually for meat] and also give some to the people in the city to buy food [so רוב money is going to be maaser money because both the money he has and the money of the people in the city is likely maaser money].  

Rashi in Pesachim [7b] adds that even though one could say that the money is from the seller [and thus lost its kedusha], nevertheless we say ספק איסורא לחומרא and the money must be treated as maaser sheni money.

However, Tosfos learns differently:

ואין לתלות דמן המוכרין נפלו וכבר מעות חולין הן שנתחללו על הבהמה

(a) Implied question: Why don't we attribute that [the coins] fell from the sellers, and they were already redeemed onto the animal [sold]?

דאזלינן בתר לוקחין דהוו רובא דמוכר אחד מוכר לכמה בני אדם

(b) Answer #1: We attribute to the buyers, for they are the majority. One seller sells to many people.

ועוד דמוקמינן להו אחזקה דהוי מעשר.

(c) Answer #2: We leave [the coins] on their Chazakah that they were Ma'aser [and we are unsure if they were redeemed].

Now from Rashi it doesn't sound like the reason we assume that the coins are maaser is because we have a רוב of איסור but rather because we go לחומרא when in doubt. 

Rashi would possibly argue with Tosfos' first answer and say that yes, there are more buyers than sellers but the doesn't help us! The issue is not the number of buyers and sellers but the MONEY - is it maaser or not. And THAT could be 50-50.  

Rashi also didn't accept Tosfos' second answer that there is a חזקה, because here the ספק has a ריעותא [weakness] since it was found in front of the sellers and the bringing of the money to the sellers is an act of preparation to take them out of their maaser status. 

The Shittah Mekubetzes writes:

עוד כתוב בתוספות ועוד דמוקמינן לה אחזקה. פירוש כיון דמספקא לן אי מלוקח אי ממוכר נפלו אזלינן בזה בתר חזקה דמלוקח נפלו שהיו בידו תחלה כי נסתפקנו ולא אזלינן בתר חזקה שהיו חולין בתחלה. גליון:

We see that he learns that the חזקה here is a חזקת מרא קמא. Since originally it was in the hands of the buyer [and was מעשר at that time], we assume that the nature of the money hasn't changed. But from the language of Tosfos who wrote "דמוקמינן להו אחזקה דהוי מעשר" it sounds like the MONEY has a חזקה and not that there is a חזקת מרא קמא.  

Now there is a question on Rashi who says that we go ספק לחומרא - as the Shittah writes [not on Rashi per se]:

"סמוך מיעוטא דלוקחים חולין למחצה והוו לוקחי מעשר מיעוטא".

We should assume that the money is chullin because we can take the minority of people who are buying chullin and half the money which belongs to the sellers - so over 50 percent will be chullin! 

Therefore we need the explanations of Tosfos. 

[עפ"י נתן פריו עמ' קמז-ח]