I would like to see a drama with a FL who is quiet but isn't considered weak.

Someone who is indifferent, and rarely talks to anyone, but opens up to the ML or her love interest.

To be honest, it doesn't have to be romance.

It can even be an anime.

Country of origin doesn't matter.

Release date also doesn't matter.

Thanks in advance :)

I just listed whatever I though that met your criteria.

The Happy Loner 

My Mister (So quiet but  incredibly expressive. Not a romance)

Just Between Lovers

Life on Mars (not a romance)

Pasta

King of Baking, Kim Tak Goo

Rebel: Thief Who Stole the People

Mask

Time

maybe weaker FLs (it depends on your opinion):

Five Enough (2nd FL)

Que Sera, Sera

The Bridal Mask (so quiet there are barely any lines)

Twelve Nights

My mister, FL is not shy at all, she's quiet, cold and very tough/strong and independent and doesnt talk to anyone but she slowly opens up to ML. it's a really good story

I totally agree on My ahjusshi. But she is somewhat like a woman who has gone through a lot thus she is cold and porcupine like. 

Also check out:

  • My Daughter sooyoung - though it took her a verryyyy long time to open up to the ML
  • Across the Ocean to See You 
  • Cinderella's Sister
  • Encounter
  • Kimi Wa Petto

Thanks for these recommendations!

Flower Boy Next Door  (I think the FL fits the bill perfectly)

My Father is Strange  (does not fit the criteria exactly, the middle daughter-she is not indifferent & is part of a big family so she has to talk, but I liked her quietness & sweetness and I loved how the idol actor fell in love with her because of those qualities)