They can try, however it is not guaranteed. The burden is on them to prove they did not break continuous residence.
https://www.uscis.gov/policymanual/HTML/PolicyManual-Volume12-PartD-Chapter3.html
Absences of more than six months but less than one year may disrupt an applicant’s continuous residence unless the applicant can prove otherwise. Accordingly, the applicant’s residence is generally the applicant’s actual physical location regardless of his or her intentions to claim it as his or her residence.
They better have abundant documented evidence of the illness, and why such an illness will take nine months away. Should have evidence to show they either filed taxes, or maintained their residence in the USA.
I'd wait five years counting from when they returned from their 2014 trip. An 8-mo trip is presumed to break the continuous residence and physical presence requirements. And, you don't apply; parents file the n400.
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