Well the type of bike has a lot to do with it, like an actual mountain bike made for trails or jumps would hold, steel over aluminum obviously. I'd say older bikes would be better, they are usually built tougher (note by the way the old frames weigh 30 pounds vs today with lightweight designs.) so I am 210 with a dented downtube for my muffler to clear. It's also steel and it's got a 2 inch downtube. It took a lot of hammering to get it dented.
It's a mongoose terrex. Has front shocks which help take some of the beating off the frame.
Look for a shorter wheelbase, as in smaller distance between where the wheels hit the ground. The smaller the distance between them generally the more sturdy the bike will be towards more extreme riding circumstances (note those little Bmx trick bikes, the small wheels and frames and wheelbases allow for more shocks without tearing the frame in half)
Not to be Uhm... Rude? But if she's so heavy she's actually breaking bikes I don't think putting a motor on it will help the cause, unless she plans on pedaling with it, which for all I know she may very well have to. I know that after I put a motor in my bike I definitely didn't start losing weight... I did however gain a few extra..
Anyway, 26 inch or smaller, smaller wheel base, and heavy steel frame, that should hold up to most people, if she has a problem with popping tires (which I did) go with the fat tire bike like a terrex, I know there are several types of bikes with fat tires, I'd suggest a steel huffy called the fortress, has 3 inch tires, cheap enough to be affordable, and after looking it over rather extensively I can see it being a suitable bike for a larger person.
I'll also note my father in law is close to 400lbs, he was able to ride my bike without it becoming scrap metal.
Good luck and it's nice to see a girl on here once and a while, still trying to get my sister to sign up so she can solve her own problems.