Is it permissible to continue owning an internet café where individual headphones are used to listen to forbidden songs, with merely putting up warning signs and disavowing the listening, knowing that it is difficult to prevent customers from doing so, and knowing that selling it would result in a significant capital loss?

It is not permissible to suffice, regarding the permissibility of opening an internet cafe, with placing signs of advice and warning against forbidden websites. Rather, it is obligatory to activate supervision and prevent anyone from using the devices for unlawful purposes. Remaining in the cafe to recover the capital, or more or less, is permissible provided the work adheres to Islamic regulations. When selling the cafe, it is not permissible to sell it except to someone who is presumed will prevent its use in ways displeasing to Allah.