It's a tough equation to solve without knowing the numbers:
What's a car the person considers "decent" going to cost ?
Does it make sense to drive rather than fly to the 2nd home ?
Is there someone in the area who can help, either with a car or checking the car left behind ?
Does it make sense to keep the old car ?
Is there an inside storage facility in the area, and its monthly/yearly cost ?

When I lived in South Jersey, I had tools & a car in a Public Storage bldg; more humid than I'd thought, and some of the tools rusted badly.
Didn't really affect the car at all, except some very slight corrosion on the aluminum parts underhood after 2 years.
Never bothered the rotors or anything else.
That place was nearly wet inside at times.