Q. Would they still get the capital gains tax exclusion?
A. Probably, but not the full $250,000 maximum.
You apparently know about the rule that usually you must live in the home 2 out of the 5 years prior to the sale, to qualify for the exclusion. There is a reduced maximum exclusion, for those who don't meet the 2 year rule due to "unforeseen circumstances". In your case (you lived in the home 17 months during the 5 year period), you maximum exclusion would be 17/24 x $250,000 = $177,000 +/-. Health reasons usually qualify as "unforeseen circumstances". But, as others have said, the IRS will look at the details of your situation.
References:
http://www.nolo.com/legal-encyclopedia/the-partial-home-sale-tax-exclusion-irs-approved-unforeseen-c...
https://www.irs.gov/publications/p523#en_US_2022_publink100073099
https://www.journalofaccountancy.com/issues/2009/nov/20091783.html
https://www.law.cornell.edu/uscode/text/26/121
http://www.nolo.com/legal-encyclopedia/qualifying-the-home-sale-exclusion-without-living-in-the-home...
