I don't know, sorry, not seen a serious proposal for this. But perhaps can help with some clarification.
Mars did have a magnetic field in the past, they think. Still has remnants of magnetism in places.
The lack of a magnetic field has two effects mainly
No protection from solar storms
Atmosphere loses water vapour - but very slowly. It would lose the water its atmosphere maybe over hundreds of thousands or millions of years. They'll know more there as they learn more about the past evolution of the Mars atmosphere.
The second reason - well to combat that you need some way of generating a magnetic field that will remain in place even in some distant future a million years from now or more when the inhabitants of Mars have lost their technology, if that happens.
But - though it might seem remote - I think it is a significant thing.
Terraforming a planet is like having a child. If you make the decision to do that, I think that ethically you commit your civilization to seeing it through so that the planet has a reasonable future, as good as any other planet. It doesn't seem ethically responsible to start off a planet that you know has an ecosystem that will fall apart a few hundred thousand or million years into the future.
Those future beings who live there are only separated from us by time, and it is because of us that they face those issues whatever they are. And maybe a somewhat wiser us, even a century later, could have arranged a far better method of terraforming or maybe done something completely different.
So, a bit hard to think of any technological solution lasting for millions of years. So, that suggests some serious level of mega-engineering, e.g. impacting giant asteroids or even impacting Mercury into Mars if you could somehow use that to start up the movements in its interior that generate the magnetic fields. Not at all impossible (e.g. sending large asteroids on repeated flybys of Mercury to change its trajectory) - but well beyond near future planetary engineering.
As for shielding from solar storms - that could be done by local magnetic generators, massive ones shielding an entire habitat - or just shielding your habitats with several meters thickness of regolith over the top - or living in caves, and doing everything by telepresence on the surface.
Anyway - though the one that people tend to focus on most, this is only one of very many issues involved in terraforming Mars.
When dealing with a whole planet then you have to think in terms of timescales of millennia and taking responsibility for a project that will take at least millenia to complete, and quite possibly much longer (on Earth it took several billion years of course) - and in a planet that is unlike Earth in many ways.
When you work with a space habitat, you can complete even a large Stanford Torus type habitat in a few decades. The projections for the Stanford Torus in the 1970s would have us making about our third or fourth torus by now, if they had done that project. And easy to fix if things go wrong. Or if it doesn't work at all, worst that happens is you have a white elephant of a non functional space habitat. Not a ruined planet.
I think we can learn a lot about planets and exoplanets and how planets work by thinking about these ideas. But I think we'd better show we can complete 30 year projects involving a couple of kilometer diameter habitats first before we even think of taking on a hundreds of thousands of years project involving a planet with same surface area as the land area of the Earth starting with a near vacuum for an atmosphere