Doesn't necessarily have to be a really poor man, could be someone who is middle class. Kinda getting worn out on the whole "rich, but cold and arrogant chaebol male heir" trope. Also would prefer if the leads stood up for themselves and didn't let people walk all over them.
Tatta Hitotsu no Koi 
Cheap Love     
Tolyo Wankei  
Boku to Star 99 Nichi

A Love to Kill -- she gets poor along the way
Lovers in Prague -- 
Into the Sunlight -- 
Manee Yard Fah --- She's a princess, he's a soldier

East of Eden -- He gets rich as story progresses 
Phoenix -- He gets rich as story progresses
Hey thank you both so much for the recommendations I'll look through them all and see what catches my interest!
hotel king
yong pal
celeb to binbo taro
+1 hotel king
+1 yong pal
i am sam
Surprised no one said Bachelor's Vegetable Store, though it is slightly complicated as to why she is rich.
That winter the wind blows