That's quite a great question.

In general, I disagree with such an arrangement. But when it comes to your perspective on whether or not you should take the offer:

If you HAVE an intern exp in the same industry as that unpaid intern:

1) Is the name of the company that big that you wish to take one more intern exp?

-> First-tier level in the industry = can consider taking it!

-> Otherwise = NO

2) Or does it provides you with a role that you never interned?

-> If yes, and it is exactly what you wanna do for your grad job = can consider taking it!

-> Otherwise, but given that you still have chance to get another intern offer = NO

-> Otherwise, but seems you only have a slim chance to get other inter offers = Try your best to drag for delaying the date you are signing a formal internship contract with them and apply for some more internships. There are still so many as you can take reference from OnMyGrad's job board.

If you HAVE NO intern exp in the same industry as that unpaid intern:

1) NO same industry exp and it is exactly what you wanna do for your grad job = can consider taking it!

2) NO same industry exp but just curious about what this industry do = Try your best to drag for delaying the date you are signing a formal internship contract with them and apply for some more internships. There are still so many as you can take reference from OnMyGrad's job board.

Hope the above helps....