Undocumented Inmigrants are a fact that the US law needs to have clear answers for at every step of the way. The identification and deportation of illegal aliens through ICE is extremely costly and unfeasible in the long run. Also, the illegal aliens spend years hiding, with no sincere incentive for coming forward to the authorities and avoid criminal activities. There should be many incentives for the illegal aliens to come forward on their own, so that they are carefully monitored by the authorities and also, live peacefully.
A special visa class UD1 needs to be defined for such people and, a 15-year path to citizenship needs to be defined by the law for every undocumented immigrant, from the moment of being identified by authorities and the visa application is approved, independently of whether the individual acquires jobs or gets married to a US Citizen in the meantime. Transitions from UD1 to other visas shall not be permitted. Approved UD1 shall be also a work permit for specific industries.
Health testing and other visa approval requirements, as with all visa applications, shall apply.
This visa application or the visa itself must be revoked immediately in case of any criminal conviction or DUI conviction, and the individual should be immediately deported.
The time of the path to citizenship should be much longer than any other process of acquiring citizenship in the US, which to my knowledge is the process I went through, coming as a student, and then working my way up (17 years to reach citizenship).