That's right — and the overcrowding story started before it even opened.
Terrell was Texas' answer to an overloaded system. In the late 19th century, the state's only psychiatric facility was in Austin, so eligible patients across Texas were often confined to county jails and poorhouses, both places incapable of treating the mentally ill.
In 1881, State Rep. John S. Wood introduced a bill for a branch in North Texas. On Feb 16, 1883, the 18th Texas Legislature passed it, specifying the new institution be somewhere north of the Texas and Pacific Railway. A 672.65-acre site a mile northeast of Terrell was selected.
It opened July 14, 1885 as the North Texas Lunatic Asylum. The original building was built according to the Kirkbride Plan — the linear, bat-wing design that was supposed to give patients light and air.
The names track how Texas thought about mental illness:

• 1885: North Texas Lunatic Asylum
• 1888: renamed North Texas Hospital for the Insane, reflecting contemporary changes in understanding and treatment
• 1925: renamed Terrell State Hospital
  To your point about capacity — it was overfull almost from day one and stayed that way for about 90 years:
• First year: 330 patients from 46 counties, next year 387. Only one-half of each wing of the main building was complete upon opening.
• 1906: 1,400 patients with a staff of 175
• By 1920: 2,300 patients — the largest hospital of its kind west of the Mississippi River
• 1945: 2,663 admitted. The population remained relatively steady between 1945 and the mid-1970s, while they kept adding wards, a laundry, a power plant, a carpentry shop, and, later, a 400-bed air-conditioned ward in 1963.
  The decline came with deinstitutionalization. By 1976, it housed 1,652 patients; by 1986, 715; and by 1988, 525, even as it remained Terrell's biggest employer.
  For nearly 140 years it has served North Texas — today 31 counties. And it's about to change again: in August 2024 Gov. Abbott broke ground on a replacement — a 415,000-square-foot, $573 million hospital expected late 2027. The new facility will have 250 beds: 165 non-maximum-security, 50 maximum-security, and 35 adolescent.
  If you drive through Terrell, you can still see some of the original patient buildings abandoned since the mid-80s — they're a stark reminder of that Kirkbride era when the state kept building, and the census kept outpacing it.