Generally, the umbrella term for the intended replacement is "community-based mental health services," and that embraces a fairly broad continuum of care, in principal.
Among the things that did not happen was sufficient funding for these to be adequately provided publicly, or assurance that non-institutionalized, privately-insured people would be likely to have these covered by private insurance. While some progress on each has been made since, access remains an issue, as does service delivery, especially with the unhoused. (One thing that was not provided for with the withdrawal of institutionalization was a replacement for the room and board inherent in institutionalization.)
There were campaigns to close the asylums based on this, but no real plan for what to replace them with.