The lady made the field hekdesh. Her husband redeemed it. Yovel started. Is the field hers or is it Cherem to Kohanim? The Gemara says "taykoo".
The Rambam concludes that, since we don't know whom it belongs to, whoever takes possesion first gets it. This is simply chulin property in dispute with neither party in possession beforehand.
Fields not redeemed by their owners are described by the Torah as "kodesh lashem kisdei hacherem, lakohanim". The Gemara on 29 amud 1 says that cherem to kohanim have the status of full hekdesh (no benefit allowed, me'ila, etc) until the kohanim actually take possession. Then they are chulin. If this is the case, this field in dispute should have a safek issur of me'ila until the kohanim take possession. It should not be a simple case of money in dispute. The lady should be forbidden to take it or use it because of safek me'ila, and the kohanim should win by default.
Moshe Perkal, Jerusalem
Your question is very sharp and insightful, Rabbi Perkal. Here are my comments on the matter for what they are worth:
Although it is not discussed openly in the Gemara or Poskim, it would seem that you are correct regarding the status of a Sedeh Achuzah that leaves the owner's hands at Yovel. It ought to be considered Hekdesh until it is delivered to the Kohanim, just like Chermei Kohanim, as is implied by the Pasuk you quoted (Vayikra 27:21) and also by the words of the Rambam (Hilchos Erchin 4:20). The Rambam writes that the field "leaves the buyer's property for Hekdesh ... and it becomes the property of the Kohanim." In that case, your question must be addressed.
In answer to your question we may point out that the Minchas Chinuch (end of Mitzvah #357) discusses whether Safek Chermei Kohanim have an Isur Hana'ah and Me'ilah or whether they are treated as a normal Safek Mamon. He suggests that there might only be an Isur Me'ilah when there is a Mitzvah to give the item to the Kohen, as with Vadai Chermei Kohanim, but not for Safek Chermei Kohanim. The Or Same'ach (end of Hilchos Terumos ch. 10) indeed finds an allusion to this reasoning in the Yerushalmi.
However, Tosfos in Yevamos (99b) implies that Me'ilah does apply to Safek Chermei Kohanim. This would indeed seem the more logical approach. The Kedushah of Chermei Kohanim is not due to the obligation to give them to the Kohen, but rather the opposite is true: The Kedushah is due to the fact that the item was given to Hekdesh (it is "Mamon Hekdesh"), and by giving it to the Kohen the Mei'lah is removed since "its Mitzvah has been fulfilled" (as the Chazon Ish here writes).
A more feasible acceptable way to answer the question might be that "Ein Me'ilah b'Karka'os," the Isur of Me'ilah does not apply to land of Hekdesh. If so, the field may be dealt with as Safek Mamon even though it is Hekdesh. It is true that if it is Hekdesh there remains an Isur Hana'ah (without Me'ilah) to derive any benefit from the field. However, that Isur may be due to the fact that the field is Mamon Hekdesh, property of Hekdesh. It is comparable to the prohibition of deriving benefit from any person's land without express permission. The principle of "ha'Motzi me'Chaveiro Alav ha'Re'ayah" would then remove the Isur of Safek Mamon Hekdesh just as it removes the Isur of Safek Gezel.
Another, simpler, answer could be that Karka is not "Mechusar Guvaina" (see Rashi to Bava Kama 12a, DH Chal Al ha'Karka). Hence, immediately upon the arrival of Yovel it is considered as though the field has already been given over to the Kohanim of that Mishmar. The Isurim of Hekdesh will thus be removed just as they are removed from any item of Chermei Kohanim that has been given to Kohanim. (When the Rambam, cited above, writes that the field "leaves the buyer's property for Hekdesh," he just means to say that the Kohanim are Zocheh "mi'Shulchan Gavo'ah," not that it actually becomes Hekdesh for a time before it is given to the Kohanim. The same is true of the verse cited in your question.)
b'Virchas Gemar Chasimah Tovah,