Private nursing home care costs about $100,000 a year. 

The National Domestic Workers Alliance estimated in 2015 that among domestic workers, 46% were foreign born: 46%, and of these 47% were unauthorized.

45% of persons over 80 experience some kind of physical or mental impairment which can (or must) be mitigated by personal care, either at home or in an institution. For those 65 or older there is a 5% probability of institutional care and for those 80 or older a 15% probability

Researchers estimate that a 10% increase in the less-educated foreign-born labor force share in a local area reduces the risk of institutionalization among the elderly by 26-29%.

From here: Immigrant Labor and the Institutionalization of the U.S.-born Elderly, by Kristin F. Butcher, Kelsey Moran & Tara Watson