I’ve always been amazed at how many people are not in the labor force and that the taxes on those who work can support everyone else.  Including those who are institutionalized.

On the other hand, I ran across a survivalist site while trying to find out how many people were in prison, and the site recommended using prisons as a defendable fortress, since most homes are totally vulnerable to attack…

Roughly 1.4% of Americans are institutionalized. In 2000:

Institutional Group Quarters: Facilities for people under formally authorized, supervised care or custody, such as correctional facilities, nursing facilities/skilled nursing facilities, in-patient hospice facilities, mental (psychiatric) hospitals, group homes for juveniles, and residential treatment centers for juveniles. Source: Peiyun She & David Stapleton. Rehabilitation Research and Training Center on Disability Demographics and Statistics Research Brief A Review of Disability Data for the Institutional Population  Cornell university.

According to the Bureau of the Census, institutional group quarters (GQs) include correctional institutions, nursing homes, and a lengthy list of othe r institutions, many of which exclusively house people with disabilities. The institutional population is a very small share of the entire population, but increased from 1.3 percent of the population in 1990 (3.3 million people) to 1.4 percent in 2000 (4.0 million people). 1 The increase was not uniform across institutional types, however. Nursing home residents, the largest institutional population in 1990, decreased from 0.71 percent of the total population to 0.61 percent, while the incarcerated population increased from 0.45 percent to 0.70 per cent, surpassing the nursing home population in size. In 2000, about 98 percen t of incarcerated persons were age 18-64, while about 90 percent of nursing home residents were age 65 or over. The percentage of the institutional population that is of working age (ages 18-64) increased from 0.98 percent in 1990 (1.5 million people) to 1.3 percent in 2000 (2.3 million people), and working-age people accounted for a much larger proportion of the institutional population in 2000 (56 percent) than in 1990 (45 percent). In 2000, a large majority of the institutional working-age population (86 percent) resided in correctional institutions, and the remaining 14% were approximately evenly split between nursing homes and other institutions

Other statistics:

Nursing & Retirement Homes   3,300,000 A relatively small number (1.5 million) and percentage (4.1%) of the 65+ population in 2009 lived in institutional settings such as nursing homes (1.3 million). However, the percentage increases dramatically with age, ranging (in 2009) from 1.1% for persons 65-74 years to 3.5% for persons 75-84 years and 13.2% for persons 85+. In addition, approximately 2.4% of the elderly lived in senior housing with at least one supportive service available to their residents.  About 11% (3.7 million) of older Medicare enrollees received personal care from a paid or unpaid source in 1999.

Prison 2,300,000 in 4,575 prisons (1 in 100 adults, 219,000 in Federal prison)

Juvenile Detention Centers: 71,000 juveniles in 2010

Mental retardation facilities: 200,000

Psychiatric Institutions: 58,000

Wheelchair Users: 1 million wheelchair users is about 1 out of 250 persons. 10,000 people every year are spinal cord injured 82% of spinal cord injuries are male 307,000 under age 44 use wheelchairs

Other references

OLMSTEAD: Reclaiming Institutionalized Lives (Abridged Version). council on disability.

INSTITUTIONAL GROUP QUARTERS
Correctional Facilities for Adults
101 Federal Detention Centers
102 Federal Prisons
103 State Prisons
104 Local Jails and Other Municipal Confinement Facilities
105 Correctional Residential Facilities
106 Military Disciplinary Barracks and Jails
Juvenile Facilities
201 Group Homes for Juveniles (Non-Correctional)
202 Residential Treatment Centers (Non-Correctional)
203 Correctional Facilities Intended for Juveniles
Nursing Facilities/Skilled-Nursing Facilities
301 Nursing Facilities/Skilled-Nursing Facilities
Other Institutional Facilities
401 Mental (Psychiatric) Hospitals and Psychiatric Units in Other Hospitals
402 Hospitals With Patients Who Have No Usual Home Elsewhere
403 In-Patient Hospice Facilities
404 Military Treatment Facilities With Assigned Patients
405 Residential Schools for People With Disabilities