Praise be to Allah.
Whoever borrows something must return it to the owner, whether it is great or small, important or insignificant, fulfilling the trust as enjoined by Allaah (interpretation of the meaning):
“Verily, Allaah commands that you should render back the trusts to those to whom they are due”
And the Prophet (peace and blessings of Allaah be upon him) said: “A trust belongs to the one who entrusted it to you.” Narrated by al-Tirmidhi (1264) and Abu Dawood (3534); classed and saheeh by al-Albaani in Saheeh al-Tirmidhi.
What you must do is return these tapes to their owners, or get in touch with them and ask them to let you off. If you cannot get in touch with them or find out about some of them, then give what you have of theirs in charity, on the basis that if you find them you will give them the choice between two things: either they will have the reward for that charity, or you will have the reward and will give them a replacement for their tapes.
Imam Ahmad (may Allaah have mercy on him) was asked about a man who had a lot of pledges and he did not know who the owners were. He said: If you cannot find out who they are, or who their heirs are, then I think that you should sell them and give their price in charity. If you find their owners after that, give them the choice between having the reward (for that charity) or being given compensation. Al-Mughni (4/264).
Shaykh al-Islam Ibn Taymiyah (may Allaah have mercy on him) said: Wealth whose owner cannot be found should be spent on the interests of the Muslims, according to the majority of scholars such as Maalik, Ahmad and others. If a person has in his possession wealth that was seized by force or that was borrowed, or that was placed in trust with him or was given as a pledge, and he cannot find the owners, then he may give it in charity on their behalf, or spend it on the interests of the Muslims, or hand it over to a just person who can spend it on the interests of the Muslims and legitimate purposes. … ‘Abd-Allaah ibn Mas’ood bought a slave woman and went into his house to get the money to pay for her, and he came out and could not find the seller. He started to go around among the poor and give the price in charity to them, and he said: “O Allaah, it is on behalf of the owner of the slave woman; if he accepts that, all well and good, otherwise it will be for me, and I will owe him the equivalent on the Day of Resurrection.”
Similarly some of the Taabi’een issued fatwas stating that whoever steals from the war booty and repents after it has been distributed, should give charity on their behalf. These fatwas were approved by the Sahaabah and Taabi’een who heard of them, such as Mu’aawiyah and others in Syria.
Majmoo’ al-Fataawa (29/321).
It says in Fataawa al-Lajnah al-Daa’imah (15/406), concerning one who is keeping a trust for someone else: If the situation is as described, then if you wish you may keep it and try to find out about the man you mentioned, or if you wish you may give what you have with you in charity to the poor, or donate it to a charitable project with the intention that the reward for that will go to the owner. Then if the owner or his heir comes to you later on, tell him what happened. If he accepts it, all will and good, otherwise give him the same amount, and you will have the reward in sha Allaah.
And Allaah knows best.