Usually in Santa Fe they deal with homeless people and release them so long as he figures out a way to show up for his probation appointments and any random Urinalyses. In some other NM towns they make you finish your term of probation inside the jail because there is literally no way to complete probation without a home and a phone and a vehicle.
In southern New Mexico, specifically Dona Ana County, the jail does not prevent release because an individual is homeless. However, upon release, it is the probationer's responsibility to comply with any remaining probation requirements or else he may face a subsequent probation violation. In my practice, I have found that probation officers are understanding and more flexible if the probationer is up front with them about his circumstances (i.e. homeless). If this is a parole violation or this person is in prison (not jail), the prison will not release the individual without a parole plan. If a person in prison is homeless, the prison will not approve a parole plan, but the person can serve out their parole time in prison and then be released.
If you have questions, either contact the jail or the specific probation office. You can locate the specific New Mexico probation office handling this matter by going to http://corrections.state.nm.us/directory/probationdir.html or calling the Central Probation and Parole Office at #(505) 827-8830.
This answers to your question is for general purposes only and does not establish an attorney-client relationship.