Usually some sort of ventilation is required to pass inspection, so I'm surprised there's nothing there. Though I guess it depends on the area - is this a home or an apartment? Its definitely a question I'd ask to the previous homeowner/landlord. There are some downdraft cooktop options with recirculating accessories, so no pipe through the slab would be required. It does make a downdraft even less effective, and you'd also need space in the cabinets plus potential mods to the countertop for a fit, so it could still be spendy.
If she doesn't cook a lot or doesn't do anything high heat/grease intensive, then it may not be a huge issue. I wouldn't recommend a bathroom fan though. As far as island hood idea, here's a link to a Whirlpool model:
https://www.whirlpool.com/kitchen/cooking/hoods/canopy/p.36-modern-glass-island-mount-range-hood.wvi75uc6ds.htmlThat would be around the floor pricing level for a basic island hood, though there might be slightly better pricing in other brand options like Frigidaire. I normally don't recommend glass canopy models since they're more of a pain to clean, but this one is convertible to recirculating if there's no place to put a pipe. If your mom prefers high heat cooking or cooks anything that leaves a lot of residual smells, this is where I'd start with hood recommendations.
~Rodney Christiansen, Factory Builder Stores