Gemara

31b - Shmuel: One may untie Chosamos attached to the ground (ropes used to lock doors, e.g. of wells), but he may not Mafki'a (unravel) them or cut them. All of these are permitted for Chosamos of Kelim. Shabbos and Yom Tov are the same for this.

Question (Beraisa): On Shabbos one may untie attached Chosamos, but he may not unravel or cut them. All of these are permitted on Yom Tov.

Answer: The Beraisa is R. Meir, who permits to make an opening. Chachamim disagree (also about Chosamos). Shmuel holds like Chachamim.

Question (Beraisa): Chachamim agree to R. Meir that on Shabbos one may untie attached Chosamos, but he may not unravel or cut them. All of these are permitted on Yom Tov.

Answer: Shmuel holds like the following Tana:

Beraisa #1: One may untie attached Chosamos, but he may not unravel them or cut them. Shabbos and Yom Tov are the same for this;

One may untie Chosamos of Kelim on Shabbos, but he may not unravel or cut them. On Yom Tov all these methods are permitted.

Question: The Seifa is unlike Shmuel!

Answer: The Seifa is R. Nechemyah, who permits moving a Keli only for its intended purpose (knives are not intended for cutting ropes).

Question: Beraisa #1 permits on Yom Tov. This is unlike R. Nechemyah!

A Beraisa forbids burning intact Kelim on Yom Tov. We were forced to establish it like R. Nechemyah!

Tana'im argue about the opinion of R. Nechemyah. (Beraisa #1 holds that he permits on Yom Tov.)

Eruvin 34b - Mishnah: If one placed an Eruv in a cabinet and lost the key, the Eruv is nevertheless valid;

R. Eliezer says, if he does not know where the key is, it is invalid.

Question: Why is it valid? (Since he cannot access his Eruv, it is as if) he and his Eruv are in different places!

Answer #1 (Rav and Shmuel): The Mishnah discusses a cabinet of arranged bricks (not cemented together). The first Tana is like R. Meir, who permits to open it. R. Eliezer holds like Chachamim, who forbid.

35a - Answer #2 (Rabah and Rav Yosef): The Mishnah discusses a wooden cabinet. The first Tana holds that it is a Keli. Building and destroying do not apply to Kelim (therefore one may break it open);

R. Eliezer holds that it is an Ohel (so one may not destroy it).

Answer #3 (Abaye and Rava): The case is, the lock is tied with ropes, and a knife is needed to break them. R. Eliezer holds like R. Nechemyah, who allows moving a Keli only for its intended purpose.

Rishonim

The Rif and Rosh (4:6) bring Shmuel's teaching.

Ran (DH Chosamos): One may untie the Chosamos because they are not permanent; they are untied constantly. One may not unravel or cut them, for Stirah applies to attached things.

Rif (Eruvin 8b): Tana'im argue about one who placed an Eruv in a cabinet and lost the key. We establish that they argue about whether or not one may use a knife to break the ropes.

R. Yehonason (Reish 9a): Even though the Mishnah in Beitzah forbids cutting attached Chosamos, that refers to on Shabbos itself. An Eruv is valid if one can access the food Bein ha'Shemashos. Chachamim hold like Rebbi, who permits Shevus Bein ha'Shemashos. This is not Stiras Ohel or Binyan. It is merely opening a door.

Rosh (Eruvin 3:5): Rashi says that Binyan and Stirah do not apply to Kelim at all. This is wrong. The Gemara asked why the Eruv is valid, because Binyan and Stirah apply to Kelim (so even Bein ha'Shemashos it is forbidden). Rabah and Rav Yosef say that the Mishnah discusses a wooden cabinet, and. Binyan and Stirah do not apply to Kelim. This refers to breaking a lock tied with ropes, or removing a door. The conclusion is that they argue about using a knife to cut a lock tied with ropes. However, one may not break a lock of wood or metal, for proper Binyan and Stirah apply to Kelim.

Poskim

Shulchan Aruch (OC 314:7): One may untie Chosamos of Kelim, i.e. the cover of a chest or cabinet tied with ropes. Alternatively, one may cut them with a knife or unravel them.

Question (R. Akiva Eiger): The Magen Avraham says that the Rambam says that one is liable for twining or unraveling ropes. How can Shmuel permit unraveling Chosamos of Kelim? Even if it is not in order to build, it is forbidden mid'Rabanan!

Answer (Bi'ur Halachah 8, DH Chosalos): The Rambam holds that 'Mafki'a' does not mean unraveling. Rather, it is tearing or lopping off.

Rebuttal (Chazon Ish 51:13): Mafki'a must be with a Keli. The Gemara established the Beraisa which forbids Mafki'a to be like R. Nechemyah, who allows moving a Keli only for its intended purpose.

Kaf ha'Chayim (51): One may not cut or unravel them if it is possible to untie them.

Shulchan Aruch (ibid.): One may not break a lock of metal or wood, for total Binyan and total Stirah apply to Kelim. This is why we may not remove hinge-pins in back of a chest if the key was lost. Some permit this. Some permit to break the lock of chests; some forbid. One may tell a Nochri to do it.

Beis Yosef (DH v'Chosav ha'Rav): R. Yakov permits removing hinge-pins in back of a chest if the key was lost. This is inferior Stirah, for nothing needs to be broken. R. Peretz disagrees, for the Gemara (Shabbos 122b) forbids removing the door to a chest, lest he bang it back in. This refers to the hinge-pins; it is proper Binyan.

Taz (7): If returning the hinge-pins is proper Binyan, removing them is proper Stirah. R. Yakov must explain that the Heter to remove the door is when there are no hinge-pins.

Question (Magen Avraham 10): The Shulchan Aruch (313:9) says that one who nails or wedges wood into wood is liable for Binyan. If so, removing hinge-pins is proper Stirah!

Answer (Magen Avraham): Perhaps that is when he makes a Keli, e.g. inserting the handle into an ax-blade. Here, it is a Keli even without the hinge-pins. All forbid nailing the hinge-pins into place; here, he is Mekalkel.

Mishnah Berurah (35): Some say that one may tell a Nochri to do it only to avoid a big loss or for a great need.

Kaf ha'Chayim (56): A case occurred, and they were unable to open the Aron Kodesh. A Nochri professional said that he would have to break the teeth of the lock. They did not allow this; they brought a Torah from another Beis ha'Keneses. Others permit, for it is Mekalkel. Shevus (telling a Nochri) of Shevus (Mekalkel) is permitted for a Mitzvah. If one can bring another Torah b'Heter, e.g. through an Eruv, this is more proper.

Kaf ha'Chayim (57): A case occurred, and the key to the lock on a door broke on a freezing day. It was permitted to tell a Nochri to remove the lock, since Stirah without intent to build is only Shevus. It is better to have a child tell him, for a child has no intent to build. It is best to tell someone to tell the Nochri to do it.

Shulchan Aruch (10): One may untie Chosamos in the ground, such as the door to a well tied by ropes, for these are not permanent knots; they will be untied. One may not unravel or cut them, due to Stirah. This is if they were not meant to be untied on Shabbos. If they were not meant to last at all, it is permitted. This is why we may unfasten a board plastered to an oven with mud, for it is not meant to last.

Source (Beis Yosef DH vesheb'Karka): The Mordechai permits if they were not meant to last at all. The Terumas ha'Deshen says that unraveling and cutting inferior Chosamos is forbidden. If they are strong, this would be forbidden even regarding Chosamos of Kelim! Therefore, even if he does not intend to make an opening, it is a Pesik Reishei. However, the Or Zaru'a cites Rashi to say that mid'Oraisa Stirah does not apply even to land when he makes a mere opening. However, it looks like Stirah mid'Rabanan. Therefore, cutting inferior Chosamos in the ground is forbidden, for it was meant to last for some time. Since it looks like Stirah, it is forbidden. A board plastered to an oven is not meant to last at all, only to preserve the heat now and be removed later. One may remove it l'Chatchilah. Rashi says that one may untie Chosamos of land because they are not permanent knots. They are meant to be untied constantly. I.e. one unties it when opening and ties it when locking. However, the door is fixed for a duration of time.

Mishnah Berurah (44): If one does not plan to untie it on Motza'ei Shabbos, it has some permanence and one may not untie it.