Liability for damages caused by one’s items that were negligently left in a public area:
Not to place a potentially damaging object in a public area: It is an act of piety for a person to hide his sharp objects [nails/glass], and any other damaging item, in an area that will not cause any potential harm/damage, such as to throw them in the river or to burn them. [This applies even if the potentially damaging object is in one owns property, and not in the public area, as it is still a potential harm for family, guests and visitors.] It is forbidden to place a potentially damaging object in the public area, unless it is publicly accepted, or one has permission from the municipality to do so.
Bodily injury: If one placed a sharp object, such as a nail or glass, in a public area, and another person became injured from the object, then if the owner did not have permission to place the item there, he is liable to pay for the bodily damage of the victim.
Monetary damage: If one placed a sharp object, such as a nail or glass, in a public area, and another person’s item became damaged from the object, then the owner is exempt from liability, even if he did not have the right to place it there, and was negligent in placing it there, or even did so deliberately. [Nevertheless, in areas that have set laws regarding these matters, it is possible to make the owner liable for monetary damages, despite the Biblical exemption. One is to speak to a Beis Din for further information.]
Initially, one is to avoid placing a damaging object in an area that can cause damage, even in one’s own property. If one was not careful to do so, and it caused damage to another person, one is liable for all bodily damage that it may cause, although is exempt from any monetary damage it causes.
If one’s clothing tore on a nail that was sticking out of someone’s Sukkah, are they liable to pay for the clothing?
No. This applies even if the Sukkah was placed in public property without permission.
 Michaber C.M. 415:3; Bava Kama 30a
 Pashut from Gemara ibid and from next Halacha which prohibits placing a hazardous object in the public area; Aruch Hashulchan 415:2
 Michaber C.M. 417:1; Bava Kama 50b
 Rama ibid; Beis Yosef 417 in name of Rashba
 Michaber C.M. 415:1 “One who hides his nails and glass in his property and it flew into the public area and damaged another person, he is liable”; Mishneh Baba Kama 30a; The above liability is only for bodily damage and not monetary damage, as brought in sources in next footnote
 A “Bur” is exempt from monetary damages of vessels: Michaber C.M. 410:21; 412:4; Tur 410; Rambam Nizkei Mamon 13:2; Mishneh Baba Kama 52a; Gemara ibid 53b and 28b; A nail or other object that damages has the same status as Bur: Michaber C.M. 411:1; 412:4-5; Rambam ibid
 The reason: As the Av Nezikin called Bor, as well as all its subcategories, is exempt from liability of monetary damage of vessels, and is only liable for damages of animals and man. [Michaber 410:21; Tur 410; Mishneh Bava Kama 52a; Gemara ibid 53b] This is learned from the verse which states the word “Shur” and comes to exclude vessels. [Baba Kama 53b]
 See the following regarding the ability of a community/country to enact stricter laws than the Torah and its Halachic binding: Rama C.M. 356:7 and Shach 356:10 regarding Dina Demalchusa Dina; Chevel Nachalaso 9:58; Baba Basra 8b; Meri ibid; Shut Harosh7:1; Rashba 2:268