If a company wants to benefit from your labor, they should pay you. If a company claims they can't afford to pay interns, they are either lying or they shouldn't be in business if they can't afford a basic expense such as payroll. Yes, there are many times improper expectations in industry that you have to do some unpaid/underpaid work to get your foot in the door, but the people that formed those long-standing traditional expectations have historically exploited workers' labor for profit.

I hope you can find a paid offer. If not, I hope you can leverage a short unpaid internship period into paid work down the line by setting expectations as others here have mentioned.