I feel like there are actually quite a few with a rich female lead (not necessarily heiresses though as many are wealthy entrepreneurs or celebrities), but in most cases ones with heiresses/wealthy female leads are melodramas (such as 49 Days, Snow Queen, That Winter the Wind Blows, A Love to Kill, Wedding, or even to a degree Angel Eyes and My Spring Days) so they don't necessarily "keep" their wealth depending on how sad the ending is... (also I'm not saying all the ones I listed necessarily have sad endings, but they are all melodramas, and I see from your profile that you hate tragedies and likely won't be interested in any of the above, but I listed them anyway for the sake of reference). Other Dramas with a rich female lead that may be more your cup of tea are:
- My Princess (Female lead finds out she's actually a princess when they decide to reinstate the monarchy
- I Do I Do (She's a successful shoe designer)
- Witch Yoo Hee (Similar plot to Take Care of the Young Lady)
- Couple or Trouble (Drama version of the Hollywood movie Overboard)
- That Fool (She's a top celebrity)
- Star's Lover (Similiar plot to That Fool)
Other dramas that fit to a degree are Ho Goo's Love (she's an elite swimmer), History of the Salaryman (only a little romance), Birth of The Rich (doesn't get the best reviews but some people really like it), Lover's in Prague (older drama and it also doesn't get the best reviews, but I plan on watching it eventually), or High Society (not sure how melodramatic [or good] it is as I also haven't seen it yet).
Note that I haven't seen all of the above (and it's not an exhaustive list), so it's possible they may not all have the character remain rich throughout the drama (and I tried to avoid listing one's you've already seen like YWCFTS and Ugly Alert). Hopefully this helps!
