There is an FAQ at the FMLA web site here:
In that page there is this paragraph:
Qualifying conditions (Q) When can an eligible employee use FMLA
A covered employer must grant an eligible employee up to a total of 12
workweeks of unpaid, job-protected leave in a 12 month period for one
or more of the following reasons:
for the birth of a son or daughter, and to bond with the newborn
child; for the placement with the employee of a child for adoption or
foster care, and to bond with that child; to care for an immediate
family member (spouse, child, or parent – but not a parent “in-law”)
with a serious health condition; to take medical leave when the
employee is unable to work because of a serious health condition; or
for qualifying exigencies arising out of the fact that the employee’s
spouse, son, daughter, or parent is on covered active duty or call to
covered active duty status as a member of the National Guard,
Reserves, or Regular Armed Forces. The FMLA also allows eligible
employees to take up to 26 workweeks of unpaid, job-protected leave in
a “single 12-month period” to care for a covered servicemember with a
serious injury or illness.
The next question is what is a "serious" medical condition. That's also covered in the FAQ:
Serious health condition (Q) What is a serious health condition?
The most common serious health conditions that qualify for FMLA leave
conditions requiring an overnight stay in a hospital or other medical
care facility; conditions that incapacitate you or your family member
(for example, unable to work or attend school) for more than three
consecutive days and have ongoing medical treatment (either multiple
appointments with a health care provider, or a single appointment and
follow-up care such as prescription medication); chronic conditions
that cause occasional periods when you or your family member are
incapacitated and require treatment by a health care provider at least
twice a year; and pregnancy (including prenatal medical appointments,
incapacity due to morning sickness, and medically required bed rest).
While a "stroke" is not specifically mentioned, the resulting medical conditions after a stroke might certainly fall under the FMLA.
If you believe you are entitled to such benefits, you should start with your HR department.