Mental institutions can expand to accept inmates, but only if security challenges are met. There will have to be changes made to those institutions because they aren't equipped to handle prisoners. Perhaps some police and law enforcement agencies can help the institutions by providing some officers to help secure the sites for their rehab stints.
Jails are overcrowded in America. They are hardly able to house, control, and maintain inmates and inmate needs. Medical attention and care in jail is very poor. Inmates with mental disorders, or mental disabilities need special treatment and care that jail can not offer. Those inmates should be rehabilitated in mental institutions.
If the inmate needs mental health assistance then I think that it should be provided to them, many crimes in the first place are committed by people who likely have mental health problems that were never properly addressed and treated, I think more focus on mental health treatment would be a net benefit for all involved.
Prison inmates currently undergo extreme hardships in prison. The prison system should be reformed to provide better health services, especially mental health services, to inmates in order to promote their reintroduction to society. This would decrease the social burden and financial costs that prisoners place on society and would promote a more effective system than we currently have.
Unless the person needs help that the prison is not equipped to provide then the inmate should just meet with a counselor at the prison. They already have counselors at prisons. There is no need to move an inmate to a mental institution. Everyone would claim they were insane to get out of prison.
No, mental institutions should not expand to accept inmates undergoing rehabilitation via prison reform, because then every prisoner will claim that they have a mental problem in order to avoid having to be in jail. It is also unfair to the non-criminals seeking medical treatment that they should have to receive it in a community of criminals.