Assalamu’alaikum Warahmatullahi Wabarakatuh
Housekeeper basically as same as an office employee or public servant. They work as well and get the salary from their effort. So, the housekeeper got their own obligation to pay zakat fitrah, if they capable of course.
If they don’t afford to pay zakat fitrah, which is actually very low, it means that there is something wrong in salary agreement with their employer. Perhaps the employer pay their salary too cheap. So the employer duty is to raise their wages, not to pay zakat. (Ahmad Sarwat, Lc/rumahfiqih.com)
See Also: Different Tax and Zakat (The Mall)