The rashba in Bava Basra 2a says that lefichoch works because of anan sahadi that if they can force each other to build a wall they will. The Gemara then asks that its obvious it goes to both and answers that when it falls into one property you might think He has a cahzoko so thats what lefichoch teaches us. He then asks that the Gemara says by a field you have to build a chozis (sign) on both sides if they build the wall together the Gemara then asks that you shouldnt build on either side then well know its both of theirs the Gemara answers one might come and build one the rashba asks on that that the chozis should be necessary in a case where it falls into one of the properties. My question is that if it belonged to one there would be a chozis on one side? (The rashba even quotes rashi as saying that)?

ב"ה Shalom, The Rashba is proving the principle that when a wall is built jointly the Halacha compels them to share what's left of the wall even if it fell into the property of one of the partners, or if one of the partners claims it for himself. Had the Mishna not told us that Halacha we might have thought that if one already claimed possession, he is "muchzak" and his partner has to bring proof to claim possession for himself. המוציא מחברו עליו הראיה. The Rashba continues to prove this principle based on the the upcoming Gemara on דף ד. There the case is that the partners agreed to make a wall in a "bikah"= valley where there is no requirement to do so. The Gemara says that a חזית must be made on both sides. And in this case too, if the wall falls , the partners divide the remaining stones. The Gemara asks, why does each one of them have to make a חזית since in any case they are to compelled to divide the remains, let neither of them make any חזית? From here the Rashba wants to prove that if not for the principle of compelling both of them to share, if one claims ownership of the stones for himself, his claim would be effective. Because otherwise what kind of question is that, that neither should make a "chazit." If he does not make a "Chazit", one of them can claim ownership?! Your question is that if it belonged to one there would be a "chozis" on one side? I think the simple answer would be, that in a case in a "bikah" where they are not required to make a wall and one made a wall on his own, the one who made the wall would make a חזית and that indeed would be his claim on ownership, since in this case the principle of כופין =compelling to share does not apply. All the best