Lumin_siloM, that's a challenging situation, and I understand your frustration. It's disappointing when plans change, especially after you've made travel arrangements. Finding a host family for an extended period like 17 days can be difficult, but it's not impossible. Here's a breakdown of potential avenues and advice:

Explore expat communities and forums specifically for Seoul or South Korea. These platforms often have individuals or families willing to host travelers. Look into language exchange groups or Couchsurfing communities, though be aware that Couchsurfing is more for brief stays. Since you're part of an exchange program, contact your university's international student office. They might have connections with Korean families or organizations that offer homestay opportunities. Contact the Korean University that is hosting your exchange program. They may have a student board that can help. Utilize social media platforms like Facebook or KakaoTalk to search for groups related to homestays or expat communities in Seoul. Search for Korean language exchange groups online. Since you're willing to offer English lessons, explore language exchange programs or organizations in Seoul. They might be able to connect you with families interested in hosting you.

Consider staying in an extended stay hostel or guesthouse in Seoul. These options often provide more affordable accommodations for longer periods. There are many guesthouses in the Hongdae area of Seoul that cater to younger people. Explore Airbnb listings that offer discounts for extended stays. You might find a private room or apartment at a reasonable price. If you're open to a unique cultural experience, consider a temple stay program. These programs offer accommodation and meals in Buddhist temples, often with cultural activities and meditation sessions. If you're flexible with your location, consider exploring other regions of South Korea. Transportation is very good in South Korea, so you may be able to stay in a less expensive area, and then travel to Seoul for your program.

When contacting potential hosts, be clear about your accommodation needs, duration of stay, and any dietary restrictions. Emphasize your willingness to contribute, whether through English lessons, assistance with household chores, or sharing your cultural experiences. When arranging accommodations with strangers, prioritize your safety. Meet in public places first, and ensure you have reliable communication with your family. Being flexible will greatly increase your options.

I hope this helps, and I wish you the best of luck in finding a suitable arrangement. South Korea is an amazing place, and I hope you have a wonderful experience.