Please recommend some Korean or Japanese drama with touching story from year 2014 - 2019

NO OLD DRAMAS BECAUSE THEY ARE DIFFICULT TO FIND

For example :

Main lead with illnese / disability  and people support him

Poor main lead lead struggle to raise money 

I mean like these ....

If there are other stories it will be ok 

  • Misaeng
  • My Ahjusshi
  • Oh My Geumbi
  • Prison Playbook
  • Beautiful world
  • Just Between Lovers
  • Mother
  • Stepmother and daughter blues
  • Hours of My Life
  • Algernon Ni Hanataba O
  • Tenno no Ryoriban
  • kounodori / Dr. Storks
  • Ashita, Mama ga Inai
  • 1 liter of Tears - I know you mentioned no old dramas, but I think these ones are easy to find. And it is super worth it

These ones are older, but since they are classics they are easy to find

  • 1 litre of tears
  • I'm sorry I love you
  • Good Life - arigatou Papa
  • Nagareboshi

2014 onwards

  • Just Between Lovers
  • Come and Hug me
  • Boku no ita Jikan
  • Marriage contract
  • Dai Renai
  • Good Doctor (j version)
  • Aogeba Toutoshi

to be honest, the best dramas with those tropes you mention are from before 2014 because those were popular tropes back in the old days and they were done well, especially in Jdramas.

+1 for 1 Litre of Tears

I will also add another classic: Kamisama mou sukoshi dake (god please give me more time). YES it's from 1998, but there's a reason people are still watching it. Truly moving, the illness is AIDS which is unique in asian dramas. It's very easy to find online.

A modern rec I didn't see on your list: It's Okay, That's Love -- ML, FL, heck... almost every single character in it has mental health issues but it focuses on ML's. the "cry" part is not in the first half but the second half.

Always movie

A Werewolf Boy movie

Fated to Love You 

Harmony  (absolutely you'll cry im sure) movie

Kill Me, Heal Me 

Remember – War of the Son 

Miracle in Cell No.7 (absolutely you'll cry im sure) movie

maybe these won't make you cry that much but they really have good story

and i saw that prison playbook suggested up there, you should watch it too

Mother the kdrama, although the original wz japanese, I highly recommend watching the Korean version 

Not all are in your time frame, but I found all of them online with no problem at all.

Mother (2009)- K film

My Mister - K drama

The Innocent Man- K drama

Secret  (2013)- K drama

3-Iron (2004)- K film

A Man and A Woman- K film

That Winter, The Wind Blows- K drama

The Servant- K film

The Beauty Inside (2015)- K film (there's the drama as well, but the movie is so much better)

Matrimonial Chaos- K drama

Departures- Japanese film

Butterfly Sleep- Japanese film

Punch (2014-2015) the main lead has a terminal illness, but this series is more than this. If you like politics and stories with corruption is for you. Even if you don't like things like that give a try! For me it's worth!