Sad Movie (2005) on Netflix

Plot summary

In Seoul, four sets of lives overlap. Jin-woo is a firefighter who has bought a ring and keeps looking for the right moment to propose to Soo-jung, a television news translator for the deaf who would rather he hesitated before rushing into danger. Soo-jung's sister Soo-eun is deaf and scarred, and works as a costumed mascot at a theme park, where an artist who comes to paint takes an interest in her while she stays behind her mask. Ha-seok has been unemployed for three years; when Suk-hyun tells him she needs a stable man, he finds work helping couples break up. Joo-young is a busy mother with little time for her son Hee-chan.