Subject to this Division, an agreement may be entered into under this Division with respect to a child who, immediately before the entering into of that agreement, had for a period of at least 2 years or an aggregate of at least 2 years in the preceding period of 3 years—
(a) been the subject of a short-term child care agreement or agreements; or
(b) been in the care of an out of home care service; or
(c) been in the care of—
(i) a registered residential service; or
(ii) a residential institution—
within the meaning of the Intellectually Disabled Persons' Services Act 1986 ; or
(d) been in the care of the Department at any premises proclaimed to be a residential program under section 19 of the Intellectually Disabled Persons' Services Act 1986 .