The standard for determining employer responsibility for paying initial unemployment benefits is not whether the employee was able to "control" his/her absences. It is whether the employer somehow "failed" the employee.
Did the employer make the attendance policy known to the employee? Did the employer document progressive counseling and discipline in relation to absences? Did the employer consider reasonable and workable requests to alter the employee's schedule without disrupting the function of the business?
If the answer to all of these questions are, "yes" then, in most states, the employer has done its due diligence and is not liable for paying unemployment. Having sick children, car problems, bad roads, oversleeping, while all understandable on occasion, are not "failures" on the part of the employer.
There is another aspect to unemployment that many people don't understand. Initial benefits are charged to the employer, meaning that the first 12 weeks (or so) of payments to a newly unemployed worker are paid fully by the employer. Those benefits are allowable in most states if and only if the employee was "wronged or failed" somehow by the employer. That is the portion that conscientious employers can and should appeal, if they believe that a termination was justified due to poor attendance or poor work habits. An example of a worker who was wronged or failed by his employer is someone who is dismissed due to overstaffing, or loses his/her job in a mass layoff.
After the first 12 weeks have either been paid by the employer to a wronged employee, or a 12 week waiting period without income has been met, then benefits are either shared by the employer and taxpayers, or paid fully by tax funds.
Employees who perform unacceptably at jobs, then are either fired with cause or quit are not entitled to any paid benefits for at least the first 12 weeks, and should not receive them from any source. Doing so only encourages irresponsible behavior by poor quality workers and costs everyone in higher product costs and taxes.
Any nursing home that fails to challenge initial unemployment claims by workers who were dismissed for poor performance is adding costs to every service they provide, resulting in higher fees to residents and/or lower pay to remaining workers. That is unconscionable.