N.Y. Labor Law § 593
(b) A claimant shall not be disqualified from receiving benefits for separation from employment due to any compelling family reason. For purposes of this paragraph, the term "compelling family reason" shall include, but not be limited to, separations related to any of the following:
(ii) the illness or disability of a member of the individual's immediate family. For the purposes of this subparagraph:
2. Refusal of employment. No weeks of total unemployment or partial unemployment shall be deemed to occur beginning with the week in which a claimant, without good cause, refuses to accept an offer of employment for which he or she is reasonably fitted by training and experience, including employment not subject to this article, until he or she has subsequently worked in employment and earned remuneration at least equal to ten times his or her weekly benefit rate. Except that claimants who are not subject to a recall date or who do not obtain employment through a union hiring hall and who are still unemployed after receiving ten weeks of benefits shall be required to accept any employment proffered that such claimants are capable of performing, provided that such employment would result in a wage not less than eighty percent of such claimant's high calendar quarter wages received in the base period and not substantially less than the prevailing wage for similar work in the locality as provided for in paragraph (d) of this subdivision. No refusal to accept employment shall be deemed without good cause nor shall it disqualify any claimant otherwise eligible to receive benefits if: