All perfect praise be to the Lord of the Worlds, and may His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
Paid internet subscription is owned by the subscriber alone; therefore, none may use it without his permission, as indicated by what the Prophet(PBUH) said when he(PBUH) delivered the sermon of the Farewell pilgrimage on the day of Sacrifice at Mina:" Verily your blood, your property and your honour are as sacred and inviolable as the sanctity of this day of yours, in this month of yours and in this town of yours."{ Related by Bukhari and Muslim}. He also said:" A Muslim's property is forbidden for others except by his permission and consent."{Musnad Al-Imam Ahmad}.".
Therefore, the permission of the subscriber should be sought before using his Wi-Fi, even if using it doesn`t affect him. However, not being protected with a password doesn`t give the people the right to use a person`s Wi-Fi because he might have forgotten to get one or might have left it running unintentionally, and a true Muslim is the one who avoids suspicious matters.
As regards the already downloaded materials, deleting them is no compensation for the owner; therefore, doing so isn`t an obligation. However, it is imperative to compensate the owner or ask for his forgiveness in order to be absolved from the liability..
We would like to point out here that it is permissible to use and download from wireless networks set up in public places since they are available and open for the public. And Allah knows best.