Landlord doesn't want to replace the jamb because it will cost about $200.
Here are the landlord's statutory duties in NC. In 42-42(b), you'll note that the landlord can't evade a duty to repair longer than 6 months even when the government won't let him make the reapir. However, there is no statutory right for the tenant to make repairs and deduct costs from the rent.
Your options are: 1) to be a pain in the ass until landlord fixes things, 2) to contract with landlord for you to hire and pay the carpenter and deduct the cost from the rent (get agreement in writing!), or 3) to sue to have the lease broken for landlord's breach of sec. 42-42(2)-(4). (Failure to provide a safe doorjamb that can't be kicked in by a 5-yr-old.)
Good luck,
Tracey
§ 42-42. Landlord to provide fit premises.
(a) The landlord shall:
(1) Comply with the current applicable building and housing codes, whether enacted before or after October 1, 1977, to the extent required by the operation of such codes; no new requirement is imposed by this subdivision (a)(1) if a structure is exempt from a current building code.
(2) Make all repairs and do whatever is necessary to put and keep the premises in a fit and habitable condition.
(3) Keep all common areas of the premises in safe condition.
(4) Maintain in good and safe working order and promptly repair all electrical, plumbing, sanitary, heating, ventilating, air conditioning, and other facilities and appliances supplied or required to be supplied by the landlord provided that notification of needed repairs is made to the landlord in writing by the tenant, except in emergency situations.
(5) Provide operable smoke detectors, either
battery-operated or electrical . . .
(b) The landlord is not released of his obligations under any part of this section by the tenant's explicit or implicit acceptance of the landlord's failure to provide premises complying with this section, whether done before the lease was made, when it was made, or after it was made, unless a governmental subdivision imposes an impediment to repair for a specific period of time not to exceed six months. Notwithstanding the provisions of this subsection, the landlord and tenant are not prohibited from making a subsequent written contract wherein the tenant agrees to perform specified work on the premises, provided that said contract is supported by adequate consideration other than the letting of the premises and is not made with the purpose or effect of evading the landlord's obligations under this Article.
§ 42-44. General remedies, penalties, and limitations.
(c) The tenant may not unilaterally withhold rent prior to a judicial determination of a right to do so.
§42-37.1. Defense of retaliatory eviction.
(a) It is the public policy of the State of North Carolina to protect tenants and other persons whose residence in the household is explicitly or implicitly known to the landlord, who seek to exercise their rights to decent, safe, and sanitary housing. Therefore, the following activities of such persons are protected by law:
(1) A good faith complaint or request for repairs to the landlord, his employee, or his agent about conditions or defects in the premises that the landlord is obligated to repair under G.S. 42-42;
(2) A good faith complaint to a government agency about a landlord's alleged violation of any health or safety law, or any regulation, code, ordinance, or State or federal law that regulates premises used for dwelling purposes;
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This is not legal advice and you are not my client. Double check everything with your own attorney and your state's laws.