The governor proposed these two changes together in her 2010 executive budget recommendations, so they are listed together here. In addition, there's actually less than meets the eye in these proposals — to some extent they represent program consolidations rather than outright eliminations of government functions.
The Office of Drug Control Policy's mission is to reduce the use of illegal drugs through a combination of social services, education and law enforcement. Under this proposal, its staff will be transferred to the Mental Health and Substance Abuse Services Administration of the Department of Community Health. The Office of Long-Term Care Supports and Services — into which the Office of Services to the Aging was recently folded — provides money to local agencies for in-home services to the elderly, various community activities and other programs for senior citizens. These functions would be "integrated" within the Department of Community Health.
The Mackinac Center recommended eliminating these programs in its 2003 and 2004 budget studies, on the basis that such government spending (and the taxes that support it) crowds out private solutions to social ills that arguably are more effective. For example, the 2004 study said the following about the drug office: "This program has laudatory objectives, but it takes money from local communities, passes it through federal and state bureaucracies, and returns the remainder of it, strings attached, to programs which often duplicate existing school-based or community-based programs. One lesson of the last 30 years of anti-drug policy is that illicit drug use is most effectively reduced through efforts financed by local community organizations and individuals."
Nevertheless, the proposals do involve genuine budget cuts, and there's virtue in consolidating and rationalizing the delivery of government services as well.